Abstract

We develop the model for the terahertz (THz) and infrared (IR) photoconductivity of graphene layers (GLs) at room temperature. The model accounts for the linear GL energy spectrum and the features of the energy relaxation and generation-recombination mechanisms inherent at room temperature, namely, the optical phonon absorption and emission and the Auger interband processes. Using the developed model, we calculate the spectral dependences of the THz and IR photoconductivity of the GLs. We show that the GL photoconductivity can change sign depending on the photon frequency, the GL doping and the dominant mechanism of the carrier momentum relaxation. We also evaluate the responsivity of the THz and IR photodetectors using the GL photoconductivity. The obtained results along with the relevant experimental data might reveal the microscopic processes in GLs, and the developed model could be used for the optimization of the GL-based photodetectors.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
    [Crossref]
  2. L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” The European Phys. J. B 56(4), 281–284 (2007).
    [Crossref]
  3. V. T. Vasko and V. Ryzhii, “Voltage and temperature dependence of conductivity in gated graphene,” Phys. Rev. B 76(23), 233404 (2007).
    [Crossref]
  4. E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett. 98(18), 186806 (2007).
    [Crossref] [PubMed]
  5. V. Vyurkov and V. Ryzhii, “Effect of Coulomb scattering on graphene conductivity,” JETP Lett. 88(5), 370–373 (2008).
    [Crossref]
  6. V. T. Vasko and V. Ryzhii, “Photoconductivity of intrinsic graphene,” Phys. Rev. B 77(19), 195433 (2008).
    [Crossref]
  7. E. H. Hwang and S. das Sarma, “Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene,” Phys. Rev. B 77(11), 115449 (2008)
    [Crossref]
  8. E. H. Hwang and S. das Sarma, “Screening induced temperature dependent transport in 2D graphene,” Phys. Rev. B 79(16), 165404 (2009).
    [Crossref]
  9. O. G. Balev, V. T. Vasko, and V. Ryzhii, “Carrier heating in intrinsic graphene by a strong dc electric field,” Phys. Rev. B 79(16), 165432 (2009).
    [Crossref]
  10. J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
    [Crossref]
  11. V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
    [Crossref]
  12. Xu Du, D. E. Prober, H. Vora, and C. Mckitterick, “Graphene-based bolometers,” 2D Mater. 1(1), 1–22 (2014).
  13. Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
    [Crossref] [PubMed]
  14. G. Skoblin, J. Sun, and A. Yurgens, “Graphene bolometer with thermoelectric readout and capacitive coupling to an antenna,” Appl. Phys. Lett. 112(6), 063501 (2018).
    [Crossref]
  15. Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
    [Crossref]
  16. T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
    [Crossref] [PubMed]
  17. S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
    [Crossref]
  18. I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
    [Crossref] [PubMed]
  19. T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
    [Crossref]
  20. K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
    [Crossref]
  21. E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
    [Crossref]
  22. G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
    [Crossref]
  23. A. Mousavian, B. Lee, A. D. Stickel, and Y.-S. Lee, “Ultrafast photocarrier dynamics in single-layer graphene driven by strong terahertz pulses,” J. Opt. Soc. Am. B 35(6), 1255–1259 (2018).
    [Crossref]
  24. M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
    [Crossref] [PubMed]
  25. V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
    [Crossref]
  26. V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
    [Crossref]
  27. D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
    [Crossref]
  28. D. Svintsov, V. Ryzhii, and T. Otsuji, “Negative dynamic Drude conductivity in pumped graphene,” Appl. Phys. Exp. 7, 115101 (2014).
    [Crossref]
  29. V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
    [Crossref]
  30. F. T. Vasko, V.V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in disordered graphene,” Phys. Rev. B 86(23), 235424 (2012).
    [Crossref]
  31. S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
    [Crossref]
  32. C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
    [Crossref]
  33. F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
    [Crossref]
  34. M. S. Foster and I. L. Aleiner, “Slow imbalance relaxation and thermoelectric transport in graphene, ” Phys. Rev. B 79(8), 085415 (2009).
    [Crossref]
  35. G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
    [Crossref]
  36. K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
    [Crossref]
  37. N. Sule, S. C. Hagness, and I. Knezevic, “Clustered impurities and carrier transport in supported graphene,” Phys. Rev. B 89(16), 165402 (2014).
    [Crossref]
  38. T. Stauber, G. Gomez-Santos, and F. Javier Garcia de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014),
    [Crossref]
  39. V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).
  40. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
    [Crossref] [PubMed]
  41. S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
    [Crossref]
  42. A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mat. 10, 569–581 (2011).
    [Crossref]
  43. V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
    [Crossref]
  44. K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
    [Crossref]
  45. H. M. Dong, W. Xu, and F. M. Peters, “Electrical generation of terahertz blackbody radiation from graphene,” Opt. Express 26(19), 24621–24626 (2018).
    [Crossref]
  46. V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].
  47. B. Zhao, J. M. Zhao, and Z. M. Zhang, “Resonance enhanced absorption in a graphene monolayer using deep metal gratings,” J. Opt. Soc. Am. B 32(6), 1176–1185 (2018).
    [Crossref]

2018 (6)

G. Skoblin, J. Sun, and A. Yurgens, “Graphene bolometer with thermoelectric readout and capacitive coupling to an antenna,” Appl. Phys. Lett. 112(6), 063501 (2018).
[Crossref]

A. Mousavian, B. Lee, A. D. Stickel, and Y.-S. Lee, “Ultrafast photocarrier dynamics in single-layer graphene driven by strong terahertz pulses,” J. Opt. Soc. Am. B 35(6), 1255–1259 (2018).
[Crossref]

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

H. M. Dong, W. Xu, and F. M. Peters, “Electrical generation of terahertz blackbody radiation from graphene,” Opt. Express 26(19), 24621–24626 (2018).
[Crossref]

B. Zhao, J. M. Zhao, and Z. M. Zhang, “Resonance enhanced absorption in a graphene monolayer using deep metal gratings,” J. Opt. Soc. Am. B 32(6), 1176–1185 (2018).
[Crossref]

2016 (4)

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

2015 (2)

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).

2014 (5)

N. Sule, S. C. Hagness, and I. Knezevic, “Clustered impurities and carrier transport in supported graphene,” Phys. Rev. B 89(16), 165402 (2014).
[Crossref]

T. Stauber, G. Gomez-Santos, and F. Javier Garcia de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014),
[Crossref]

Xu Du, D. E. Prober, H. Vora, and C. Mckitterick, “Graphene-based bolometers,” 2D Mater. 1(1), 1–22 (2014).

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
[Crossref]

D. Svintsov, V. Ryzhii, and T. Otsuji, “Negative dynamic Drude conductivity in pumped graphene,” Appl. Phys. Exp. 7, 115101 (2014).
[Crossref]

2013 (5)

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

2012 (4)

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

F. T. Vasko, V.V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in disordered graphene,” Phys. Rev. B 86(23), 235424 (2012).
[Crossref]

2011 (3)

V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
[Crossref]

A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mat. 10, 569–581 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
[Crossref]

2010 (1)

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

2009 (6)

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

M. S. Foster and I. L. Aleiner, “Slow imbalance relaxation and thermoelectric transport in graphene, ” Phys. Rev. B 79(8), 085415 (2009).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

E. H. Hwang and S. das Sarma, “Screening induced temperature dependent transport in 2D graphene,” Phys. Rev. B 79(16), 165404 (2009).
[Crossref]

O. G. Balev, V. T. Vasko, and V. Ryzhii, “Carrier heating in intrinsic graphene by a strong dc electric field,” Phys. Rev. B 79(16), 165432 (2009).
[Crossref]

2008 (6)

V. Vyurkov and V. Ryzhii, “Effect of Coulomb scattering on graphene conductivity,” JETP Lett. 88(5), 370–373 (2008).
[Crossref]

V. T. Vasko and V. Ryzhii, “Photoconductivity of intrinsic graphene,” Phys. Rev. B 77(19), 195433 (2008).
[Crossref]

E. H. Hwang and S. das Sarma, “Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene,” Phys. Rev. B 77(11), 115449 (2008)
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

2007 (4)

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” The European Phys. J. B 56(4), 281–284 (2007).
[Crossref]

V. T. Vasko and V. Ryzhii, “Voltage and temperature dependence of conductivity in gated graphene,” Phys. Rev. B 76(23), 233404 (2007).
[Crossref]

E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett. 98(18), 186806 (2007).
[Crossref] [PubMed]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
[Crossref]

Adam, S.

E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett. 98(18), 186806 (2007).
[Crossref] [PubMed]

Aldazabal, I.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Aleiner, I. L.

M. S. Foster and I. L. Aleiner, “Slow imbalance relaxation and thermoelectric transport in graphene, ” Phys. Rev. B 79(8), 085415 (2009).
[Crossref]

Aleshkin, V. Y.

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

Aleshkin, V. Ya.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

Alymov, G.

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

Arnau, A.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Aumayr, F.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Balandin, A. A.

A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mat. 10, 569–581 (2011).
[Crossref]

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

Balev, O. G.

O. G. Balev, V. T. Vasko, and V. Ryzhii, “Carrier heating in intrinsic graphene by a strong dc electric field,” Phys. Rev. B 79(16), 165432 (2009).
[Crossref]

Banman, A. R.

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

Bao, W.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

Basov, D. N.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Baudisch, M.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Bayer, B. C.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Biegert, J.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Bonn, M.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Borisov, A. G.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Boubanga-Tombet, S.

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

Boubanga-Tombet, S. A.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

Cacho, C.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Calizo, I.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

Castro Neto, A. H.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Cavalleri, A.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Centeno, A.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Chan, S.

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

Charasheyhar, M.

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

Chen, J.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Chen, Y.

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

Chen, Yi

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Chen, Z.

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

Cox, J. D.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

das Sarma, S.

E. H. Hwang and S. das Sarma, “Screening induced temperature dependent transport in 2D graphene,” Phys. Rev. B 79(16), 165404 (2009).
[Crossref]

E. H. Hwang and S. das Sarma, “Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene,” Phys. Rev. B 77(11), 115449 (2008)
[Crossref]

de Abajo, F. J. G.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Docherty, C. J.

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Dong, H. M.

Du, Xu

Xu Du, D. E. Prober, H. Vora, and C. Mckitterick, “Graphene-based bolometers,” 2D Mater. 1(1), 1–22 (2014).

Dubinov, A. A.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

Elorza, A. Z.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Facsko, S.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Falkovsky, L. A.

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” The European Phys. J. B 56(4), 281–284 (2007).
[Crossref]

Fei, Z.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Fogler, M. M.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Foster, M. S.

M. S. Foster and I. L. Aleiner, “Slow imbalance relaxation and thermoelectric transport in graphene, ” Phys. Rev. B 79(8), 085415 (2009).
[Crossref]

Fukushima, T.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

Gao, T.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

George, P. A.

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

Ghosh, S.

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

Gierz, I.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Goldflam, M. D.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Gomez-Santos, G.

T. Stauber, G. Gomez-Santos, and F. Javier Garcia de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014),
[Crossref]

Gruber, E.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Guinea, F.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Hagness, S. C.

N. Sule, S. C. Hagness, and I. Knezevic, “Clustered impurities and carrier transport in supported graphene,” Phys. Rev. B 89(16), 165402 (2014).
[Crossref]

Han, Q.

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

Han, Qi

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Han, Wei

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

Heinz, T. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

Hertz, L. M.

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Heyman, J. N.

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

Hierzenberger, A.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Hone, J.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Hu, J.

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

Hupalo, M.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

Hwang, E. H.

E. H. Hwang and S. das Sarma, “Screening induced temperature dependent transport in 2D graphene,” Phys. Rev. B 79(16), 165404 (2009).
[Crossref]

E. H. Hwang and S. das Sarma, “Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene,” Phys. Rev. B 77(11), 115449 (2008)
[Crossref]

E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett. 98(18), 186806 (2007).
[Crossref] [PubMed]

Javier Garcia de Abajo, F.

T. Stauber, G. Gomez-Santos, and F. Javier Garcia de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014),
[Crossref]

Jensen, S. A.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Johnston, M. B.

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Joyce, H. J.

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Kaminski, Z. S.

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

Katsnelson, M. I.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

Kawakami, R. K.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

Kazansky, A. K.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Keilmann, F.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Knezevic, I.

N. Sule, S. C. Hagness, and I. Knezevic, “Clustered impurities and carrier transport in supported graphene,” Phys. Rev. B 89(16), 165402 (2014).
[Crossref]

Kohler, A.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Koppens, F.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Koppens, F. H.L.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Kozubek, R.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Krasheninnikov, A. V.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Lau, C. N.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

Lee, B.

Lee, Y.-S.

Leiman, V. G.

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

Levitov, L. S.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Li, L. J.

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Li, T.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

Libish, F.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Lin, C. T.

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Liu, G.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Liu, M. K.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Liu, Z.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Lui, Ch. H.

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

Luo, L.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

Lv, Q.

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

Mak, K. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

Marini, A.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Massari, A. M.

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

Massicotte, M.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

McCreary, K. M.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

Mckitterick, C.

Xu Du, D. E. Prober, H. Vora, and C. Mckitterick, “Graphene-based bolometers,” 2D Mater. 1(1), 1–22 (2014).

McLeod, A. S.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Miao, F.

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

Misewich, J. A.

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

Mitin, V.

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

Mitin, V.V.

F. T. Vasko, V.V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in disordered graphene,” Phys. Rev. B 86(23), 235424 (2012).
[Crossref]

Mitrano, M.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Mousavian, A.

Ni, G. X.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Nicholas, R. J.

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Nika, D. L

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Otsuji, T.

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).

D. Svintsov, V. Ryzhii, and T. Otsuji, “Negative dynamic Drude conductivity in pumped graphene,” Appl. Phys. Exp. 7, 115101 (2014).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
[Crossref]

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

F. T. Vasko, V.V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in disordered graphene,” Phys. Rev. B 86(23), 235424 (2012).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
[Crossref]

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

Ozyilmaz, B.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Pesquera, A.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Peters, F. M.

Petersen, J. C.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Petuya, R.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Pi, K.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

Pokatilov, E. P.

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

Ponomarev, D. S.

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

Prober, D. E.

Xu Du, D. E. Prober, H. Vora, and C. Mckitterick, “Graphene-based bolometers,” 2D Mater. 1(1), 1–22 (2014).

Rana, F.

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

Robinson, J. T.

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

Ryabova, N.

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

Ryzhii, M.

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
[Crossref]

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

Ryzhii, V.

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
[Crossref]

D. Svintsov, V. Ryzhii, and T. Otsuji, “Negative dynamic Drude conductivity in pumped graphene,” Appl. Phys. Exp. 7, 115101 (2014).
[Crossref]

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

F. T. Vasko, V.V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in disordered graphene,” Phys. Rev. B 86(23), 235424 (2012).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

O. G. Balev, V. T. Vasko, and V. Ryzhii, “Carrier heating in intrinsic graphene by a strong dc electric field,” Phys. Rev. B 79(16), 165432 (2009).
[Crossref]

V. T. Vasko and V. Ryzhii, “Photoconductivity of intrinsic graphene,” Phys. Rev. B 77(19), 195433 (2008).
[Crossref]

V. Vyurkov and V. Ryzhii, “Effect of Coulomb scattering on graphene conductivity,” JETP Lett. 88(5), 370–373 (2008).
[Crossref]

V. T. Vasko and V. Ryzhii, “Voltage and temperature dependence of conductivity in gated graphene,” Phys. Rev. B 76(23), 233404 (2007).
[Crossref]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
[Crossref]

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

Sarma, S. D.

E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett. 98(18), 186806 (2007).
[Crossref] [PubMed]

Satou, A.

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
[Crossref]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

Schleberger, M.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Schmalian, J.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

Sfeir, M. Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

Sharavaraman, S.

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

Shur, M. S.

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

Shur, M.S.

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).

Silva, F.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Skoblin, G.

G. Skoblin, J. Sun, and A. Yurgens, “Graphene bolometer with thermoelectric readout and capacitive coupling to an antenna,” Appl. Phys. Lett. 112(6), 063501 (2018).
[Crossref]

Smejkal, V.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Song, J.C.W.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Spencer, M. G.

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

Springate, E.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Starke, U.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Stauber, T.

T. Stauber, G. Gomez-Santos, and F. Javier Garcia de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014),
[Crossref]

Stein, J. D.

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

Stickel, A. D.

Stohr, A.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Strait, J. H.

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

Sule, N.

N. Sule, S. C. Hagness, and I. Knezevic, “Clustered impurities and carrier transport in supported graphene,” Phys. Rev. B 89(16), 165402 (2014).
[Crossref]

Sun, J.

G. Skoblin, J. Sun, and A. Yurgens, “Graphene bolometer with thermoelectric readout and capacitive coupling to an antenna,” Appl. Phys. Lett. 112(6), 063501 (2018).
[Crossref]

Svintsov, D.

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
[Crossref]

D. Svintsov, V. Ryzhii, and T. Otsuji, “Negative dynamic Drude conductivity in pumped graphene,” Appl. Phys. Exp. 7, 115101 (2014).
[Crossref]

Swartz, A. G.

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

Tang, N.

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

Teichmann, S.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Teweldebrhan, D.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

Tielrooij, K. J.

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

Tringides, M. C.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

Turcu, I. E.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Varlamov, A. A.

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” The European Phys. J. B 56(4), 281–284 (2007).
[Crossref]

Vasko, F. T.

F. T. Vasko, V.V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in disordered graphene,” Phys. Rev. B 86(23), 235424 (2012).
[Crossref]

Vasko, V. T.

O. G. Balev, V. T. Vasko, and V. Ryzhii, “Carrier heating in intrinsic graphene by a strong dc electric field,” Phys. Rev. B 79(16), 165432 (2009).
[Crossref]

V. T. Vasko and V. Ryzhii, “Photoconductivity of intrinsic graphene,” Phys. Rev. B 77(19), 195433 (2008).
[Crossref]

V. T. Vasko and V. Ryzhii, “Voltage and temperature dependence of conductivity in gated graphene,” Phys. Rev. B 76(23), 233404 (2007).
[Crossref]

Vora, H.

Xu Du, D. E. Prober, H. Vora, and C. Mckitterick, “Graphene-based bolometers,” 2D Mater. 1(1), 1–22 (2014).

Vyurkov, V.

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
[Crossref]

V. Vyurkov and V. Ryzhii, “Effect of Coulomb scattering on graphene conductivity,” JETP Lett. 88(5), 370–373 (2008).
[Crossref]

Wagner, M.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Wang, J.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

Wang, L.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Wang, Y.

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

Watanabe, T.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

Wilhelm, R. A.

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Wu, X.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Wu, Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

Xia, Y.

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

Xu, W.

Xu, X.

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

Yabe, Y.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

Yang, X.

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

Ye, H.

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

Yin, D.

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

Yin, W.

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

Yu, D.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Yurchenko, S. O.

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

Yurgens, A.

G. Skoblin, J. Sun, and A. Yurgens, “Graphene bolometer with thermoelectric readout and capacitive coupling to an antenna,” Appl. Phys. Lett. 112(6), 063501 (2018).
[Crossref]

Zhang, J.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

Zhang, R.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Zhang, Y.

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

Zhang, Z. M.

Zhao, B.

Zhao, J. M.

Zhu, T.

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Zhuang, S.

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

2D Mater. (1)

Xu Du, D. E. Prober, H. Vora, and C. Mckitterick, “Graphene-based bolometers,” 2D Mater. 1(1), 1–22 (2014).

AIP Advances (1)

S. Zhuang, Y. Chen, Y. Xia, N. Tang, X. Xu, J. Hu, and Z. Chen, “Coexistence of negative photoconductivity and hysteresis in semiconducting graphene,” AIP Advances 6(4), 045214 (2016).
[Crossref]

Appl. Phys. Exp. (1)

D. Svintsov, V. Ryzhii, and T. Otsuji, “Negative dynamic Drude conductivity in pumped graphene,” Appl. Phys. Exp. 7, 115101 (2014).
[Crossref]

Appl. Phys. Lett. (2)

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nano-electronic circuits,” Appl. Phys. Lett. 92(15), 151911 (2008).
[Crossref]

G. Skoblin, J. Sun, and A. Yurgens, “Graphene bolometer with thermoelectric readout and capacitive coupling to an antenna,” Appl. Phys. Lett. 112(6), 063501 (2018).
[Crossref]

Chin. Phys. B (1)

Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25(11), 118103 (2016).
[Crossref]

J. Appl. Phys. (4)

J. N. Heyman, J. D. Stein, Z. S. Kaminski, A. R. Banman, A. M. Massari, and J. T. Robinson, “Carrier heating and negative photoconductivity in graphene,” J. Appl. Phys. 117(1), 015101 (2015).
[Crossref]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
[Crossref]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Y. Aleshkin, “Feasibility of terahertz lasing in optically pumped epitaxial multiple graphene layer structures,” J. Appl. Phys. 106(8), 084507 (2009).
[Crossref]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. D: Appl. Phys. (1)

V. Ryzhii, T. Otsuji, M. Ryzhii, N. Ryabova, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Graphene terahertz uncooled bolometers,” J. Phys. D: Appl. Phys. 46, 065102 (2013).
[Crossref]

JETP Lett. (1)

V. Vyurkov and V. Ryzhii, “Effect of Coulomb scattering on graphene conductivity,” JETP Lett. 88(5), 370–373 (2008).
[Crossref]

Jpn. J. Appl. Phys. (1)

V. Ryzhii, M. Ryzhii, V. Mitin, A. Satou, and T. Otsuji, “Effect of heating and cooling of photogenerated electron-hole plasma in optically pumped graphene on population inversion,” Jpn. J. Appl. Phys. 50(9), 094001 (2011).
[Crossref]

Lithuanian J. Phys. (1)

V. Ryzhii, T. Otsuji, M. Ryzhii, V. Mitin, and M.S. Shur, “Effect of indirect interband transitions on terahertz conductivity in “decorated ” graphene bilayer heterostructures,” Lithuanian J. Phys. 55(4), 243–248 (2015).

Nano Lett. (1)

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett.,  8(3), 902–907 (2008).
[Crossref] [PubMed]

Nat. Comm (1)

C. J. Docherty, C. T. Lin, H. J. Joyce, R. J. Nicholas, L. M. Hertz, L. J. Li, and M. B. Johnston, “Extreme sensitivity of graphene photoconductivity to environmental gases,” Nat. Comm. 3, 1228 (2012).
[Crossref]

Nat. Comm. (1)

E. Gruber, R. A. Wilhelm, R. Petuya, V. Smejkal, R. Kozubek, A. Hierzenberger, B. C. Bayer, I. Aldazabal, A. K. Kazansky, F. Libish, A. V. Krasheninnikov, M. Schleberger, S. Facsko, A. G. Borisov, A. Arnau, and F. Aumayr, “Ultrafast electronic response of graphene to a strong and localized electric field,” Nat. Comm. 7, 13948 (2016).
[Crossref]

Nat. Commun. (1)

M. Baudisch, A. Marini, J. D. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. J. G. de Abajo, and J. Biegert, “Ultrafast nonlinear optical response of Dirac fermions in graphene,” Nat. Commun. 9, 1018 (2018).
[Crossref] [PubMed]

Nat. Mat. (1)

A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mat. 10, 569–581 (2011).
[Crossref]

Nat. Mater. (1)

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. E. Turcu, E. Springate, A. Stohr, A. Kohler, U. Starke, and A. Cavalleri, “Snapshots of nonequilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Nat. Photon. (1)

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Ozyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photon. 10, 244–247 (2016).
[Crossref]

Nat. Phys. (1)

K. J. Tielrooij, J.C.W. Song, S. A. Jensen, A. Centeno, A. Pesquera, A. Z. Elorza, M. Bonn, L. S. Levitov, and F. H.L. Koppens, “Photoexcitation cascade and multiple hot-carrier generation in graphene,” Nat. Phys. 9(4), 248–252 (2013).
[Crossref]

New J. Phys. (1)

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga-Tombet, A. Satou, A. A. Dubinov, V. Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmonpolaritons on terahertz stimulated emission in optically pumped monolayer graphene,“ New J. Phys. 15(7), 07503 (2013).
[Crossref]

Opt. Expess (1)

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Expess 22(17), 19873–19686 (2014).
[Crossref]

Opt. Express (1)

Phys. Rev. B (12)

F. T. Vasko, V.V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in disordered graphene,” Phys. Rev. B 86(23), 235424 (2012).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85(3), 035443 (2012).
[Crossref]

F. Rana, P. A. George, J. H. Strait, S. Sharavaraman, M. Charasheyhar, and M. G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11)(11), 115447 (2009).
[Crossref]

M. S. Foster and I. L. Aleiner, “Slow imbalance relaxation and thermoelectric transport in graphene, ” Phys. Rev. B 79(8), 085415 (2009).
[Crossref]

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

K. M. McCreary, K. Pi, A. G. Swartz, Wei Han, W. Bao, C. N. Lau, F. Guinea, M. I. Katsnelson, and R. K. Kawakami, “Effect of cluster formation on graphene mobility,” Phys. Rev. B 81(11), 115453 (2010).
[Crossref]

N. Sule, S. C. Hagness, and I. Knezevic, “Clustered impurities and carrier transport in supported graphene,” Phys. Rev. B 89(16), 165402 (2014).
[Crossref]

V. T. Vasko and V. Ryzhii, “Photoconductivity of intrinsic graphene,” Phys. Rev. B 77(19), 195433 (2008).
[Crossref]

E. H. Hwang and S. das Sarma, “Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene,” Phys. Rev. B 77(11), 115449 (2008)
[Crossref]

E. H. Hwang and S. das Sarma, “Screening induced temperature dependent transport in 2D graphene,” Phys. Rev. B 79(16), 165404 (2009).
[Crossref]

O. G. Balev, V. T. Vasko, and V. Ryzhii, “Carrier heating in intrinsic graphene by a strong dc electric field,” Phys. Rev. B 79(16), 165432 (2009).
[Crossref]

V. T. Vasko and V. Ryzhii, “Voltage and temperature dependence of conductivity in gated graphene,” Phys. Rev. B 76(23), 233404 (2007).
[Crossref]

Phys. Rev. Lett. (4)

E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett. 98(18), 186806 (2007).
[Crossref] [PubMed]

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012).
[Crossref] [PubMed]

T. Stauber, G. Gomez-Santos, and F. Javier Garcia de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014),
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, Ch. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref]

Rev. Mod. Phys. (1)

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Sci Rep. (1)

Qi Han, T. Gao, R. Zhang, Yi Chen, J. Chen, G. Liu, Y. Zhang, Z. Liu, X. Wu, and D. Yu, “Highly sensitive hot electron bolometer based on disordered graphene,” Sci Rep. 3, 3533 (2013).
[Crossref] [PubMed]

The European Phys. J. B (1)

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” The European Phys. J. B 56(4), 281–284 (2007).
[Crossref]

Other (1)

V. Ryzhii, M. Ryzhii, D. S. Ponomarev, V. G. Leiman, V. Mitin, M. S. Shur, and T. Otsuji, “Negative photoconductivity and hot-carrier bolometric detection of terahertz radiation in graphene-phosphorene hybrid structures,” J. Appl. Phys.124, in press; arXiv:808.09083 [cond-mat.mes-hall].

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Figures (5)

Fig. 1
Fig. 1 Upper panel: the normalized carrier temperature variation (TT0)/T0 (dashed lines) for different values of the parameter b (upper panel) and τ0 = 1 ps and the quasi-Fermi energy μ/T (solid line) for b = 0.1 and τ0 = 1 ps. Lower panel: the normalized carrier temperature variation (TT0)/T0 (dashed line) for b = 0.1 and τ0 = 1 ps and the quasi-Fermi energy μ/T (solid lines) for b = 1 and different τ0.
Fig. 2
Fig. 2 The normalized GL photoconductivity ΔσΩ/σ00 as functions of the photon energy ħΩ (dominant short-range scattering) for different b = τOpt/τAuger and τ0 = 1 ps (left panel) and different τ0 and b = 0.1 (right panel).
Fig. 3
Fig. 3 The same as in Fig. 2 but in the case of dominant long-range scattering: for b = τOpt/τAuger and τ0 = 1 ps (left panel) and for τ0 and b = 0.1 (right panel).
Fig. 4
Fig. 4 The spectral characteristics of the responsivity, RΩ/R, of the GL-based photodetectors with dominant short-range scattering at different b and τ0 = 1 ps (left panel) and different τ0 and b = 0.1 (right panel).
Fig. 5
Fig. 5 The same as in Fig. 4 but for the photodetectors with the dominant long-range scattering.

Equations (36)

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σ Ω = e 2 T 0 τ 0 π 2 ( T T 0 ) l + 1 0 d ξ ξ l + 1 ( 1 + Ω 2 τ 0 2 ( T / T 0 ) 2 l ξ 2 l ) d d ξ [ f e ( ξ ) + f h ( ξ ) ] .
σ Ω = σ 00 ( 1 + Ω 2 τ 2 ) [ 1 exp ( μ e / T ) + 1 + 1 exp ( μ h / T ) + 1 ] .
σ Ω = 2 σ 00 ( 1 + Ω 2 τ 2 ) 1 [ exp ( μ / T ) + 1 ] .
σ Ω = 4 σ 00 ( 1 + Ω 2 τ 2 ) ( T T 0 ) 2 1 ( μ T ) ,
1 ( η ) = 0 d ξ ξ exp ( ξ η ) + 1
G Auger + G Opt + G Ac + G Rad = 0 .
1 τ O p t { exp [ 2 μ T + ω 0 ( 1 T 0 1 T ) ] 1 } + 1 τ Auger [ exp ( 2 μ T ) 1 ] = β inter I Ω Σ 0 .
1 τ Opt { exp [ 2 μ T + ω 0 ( 1 T 0 1 T ) ] 1 } + 1 τ Opt intra { exp [ ω 0 ( 1 T 0 1 T ) ] 1 } = ( β intra + β inter ) Ω I Ω ω 0 Σ 0 .
1 τ Opt 2 μ T + ( 1 τ Opt + 1 τ Opt intra ) ω 0 ( T T 0 ) T 0 2 ( β 0 intra + β 0 inter ) Ω I Ω ω 0 Σ 0 .
( 1 τ Opt + 1 τ Auger ) 2 μ T + 1 τ Opt ω 0 ( T T 0 ) T 0 2 = β 0 inter I Ω Σ 0 ,
μ T [ ( β 0 inter + β 0 intra ) ( Ω ω 0 ) β 0 inter ( 1 + a ) ] τ R I Ω 2 Σ 0 .
T T 0 T 0 [ ( β 0 inter + β 0 intra ) ( Ω ω 0 ) ( 1 + b ) β 0 inter ] T 0 ω 0 τ R I Ω Σ 0 .
1 τ R = ( 1 + a ) τ Auger + a τ Opt ,
T T 0 T 0 1 ( a + b + a b ) T 0 ω 0 [ tanh ( Ω 4 T 0 ) ( Ω ω 0 ( 1 + b ) 1 ) + D 0 ( 1 + b ) ( 1 + 3 Ω 2 τ 0 2 / π 2 ) ( Ω ω 0 ) ] I Ω I ¯ Ω ,
μ T 1 2 ( a + b + a b ) T 0 ω 0 [ tanh ( Ω 4 T 0 ) ( Ω ω 0 1 a ) + D 0 ( 1 + 3 Ω 2 τ 0 2 / π 2 ) ( Ω ω 0 ) ] I Ω I ¯ Ω .
I ¯ Ω = κ Σ 0 π α τ Opt .
T T 0 T 0 1 ( 1 + a ) T 0 ω 0 ( Ω ω 0 ) [ tanh ( Ω 4 T 0 ) + D 0 ( 1 + 3 Ω 2 τ 0 2 / π 2 ) ] I Ω I ¯ Ω 0 .
Δ σ Ω σ 00 μ 2 T ,
Δ σ Ω σ 00 1 4 ( a + b + a b ) [ tanh ( Ω 4 T 0 ) ( Ω ω 0 1 a ) + D 0 ( 1 + 3 Ω 2 τ 0 2 / π 2 ) ( Ω ω 0 ) ] I Ω I ¯ Ω .
Ω 0 π 3 τ 0 D 0 ( 1 + a ) 4 T 0 ω 0 1 16 π 3 ( 1 + a ) ω 0 τ 0 T 0 τ 0 1 / 2
Ω 1 ( 1 + a ) ω 0 [ 1 4 π 2 3 ( 1 + a 2 ) ω 0 τ 0 T 0 ω 0 ] ( 1 + a ) ω 0 .
σ Ω = σ 00 ( 1 + Ω 2 τ 0 2 ) ( T T 0 ) 2 [ π 2 3 + 4 μ T ln 2 + ( μ T ) 2 ] π 2 3 σ 00 ( 1 + Ω 2 τ 0 2 ) ( T T 0 ) 2 .
Δ σ Ω σ 00 2 π 2 3 ( T T 0 ) T 0 .
Δ σ Ω σ 00 2 π 2 3 ( a + b + a b ) T 0 ω 0 [ tanh ( Ω 4 T 0 ) ( Ω ω 0 ( 1 + b ) 1 ) + D 0 ( 1 + b ) ( 1 + Ω 2 τ 0 2 ) ( Ω ω 0 ) ] I Ω I ¯ Ω .
R Ω R D 0 ( a + b + a b ) ( T 0 Ω ) | tanh ( Ω 4 T 0 ) ( Ω ω 0 1 a ) + D 0 ( 1 + 3 Ω 2 τ 0 2 / π 2 ) ( Ω ω 0 ) | ,
R Ω R 2 π 2 D 0 3 ( a + b + a b ) ( T 0 2 ω 0 Ω ) | tanh ( Ω 4 T 0 ) ( Ω ω 0 ( 1 + b ) 1 ) + D 0 ( 1 + b ) ( 1 + 3 Ω 2 τ 0 2 / π 2 ) ( Ω ω 0 ) | ,
R = 3 α 16 κ e 2 τ Opt v W 2 E T 0 3 L
β A inter = π α 2 κ [ tanh ( Ω / 2 μ 0 2 T 0 ) + tanh ( Ω / 2 + μ 0 2 T 0 ) ]
β A intra = 4 π α D 0 κ ( 1 + Ω 2 τ 0 2 T 0 2 / μ 0 2 ) ,
exp [ ω 0 ( 1 T 0 1 T ) ] = 1 + [ β A intra ( Ω ω 0 ) + β A inter ( Ω ω 0 1 ) ] I Ω Σ A τ Opt intra .
exp [ μ e + μ h T + ω 0 ( 1 T 0 1 T ) ] = 1 + β A inter I Ω Σ A τ Opt .
T T 0 T 0 T 0 ω 0 [ β A intra ( Ω ω 0 ) + β A inter ( Ω ω 0 1 ) ] I Ω Σ A τ Opt intra ,
μ e + μ h T + ω 0 ( T T 0 ) T 0 T = β A inter I Ω Σ A τ Opt .
U = ( T T 0 ) 2 [ 1 ( μ h T ) 1 ( μ e T ) ] .
μ T μ 0 T 0 [ 1 ( 1 + π 2 3 T 0 2 μ 0 2 ) ( T T 0 ) T 0 ] μ 0 T 0 [ 1 ( T T 0 ) T 0 ] .
Δ σ Ω σ 00 Σ 0 a Σ A exp ( μ 0 T 0 ) { [ tanh ( Ω / 2 μ 0 2 T 0 ) + tanh ( Ω / 2 + μ 0 2 T 0 ) ] ( Ω ω 0 1 a ) + D 0 ( 1 + Ω 2 τ 0 2 T 0 2 / μ 0 2 ) ( Ω ω 0 ) } I Ω I ¯ Ω ,

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