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The negative dynamic conductivity of graphene in THz range makes it to be a promise medium in THz radiation and amplification. This paper proposes electrically pumped multiple graphene layer structures with split gates, sets up the theory model of electrically induced n-i-p junction, calculates the ac conductivity associated with the interband and intraband transitions under the conditions of population inversion, discusses the bias voltage, gate voltage, number of graphene layers and the momentum relaxation time dependences of ac conductivity. It is shown that the real part of dynamic conductivity within terahertz range can be negative in certain conditions, namely, interband radiation is greater than the intraband absorption, which demonstrates the feasibility of taking electrically pumped multiple graphene layer structures with split gates as an active medium in radiating terahertz coherent source.
[1] Zhang Y, Tan Y W, Stormer H L, Kim P. 2005 Nature (London) 438 201
[2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Dubonos S V, Firsov A A 2005 Nature (London) 438 197
[3] Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620
[4] Geim A K, Novoselov K S 2007 Nat. Mater. 6 183
[5] Ryzhii V Ryzhii M, Otsuji T 2007 J. Appl. Phys. 101 083114
[6] Kang C Y, Tang J, Li L M 2011 Acta Phys. Sin. 047302 (in Chinese) [康朝阳, 唐军, 李利民 2011 {物理学报 60 047302]
[7] Jin Z F, Tong G P, Jiang Y J 2009 Acta Phys. Sin. 58 8537 (in Chinese) [金子飞, 童国平, 蒋永进 2009 {物理学报 58 8537]
[8] Pan H Z, Xu M, Chen L 2010 Acta Phys. Sin. 59 6443 (in Chinese) [潘洪哲, 徐明, 陈丽 2010 {物理学报 59 6443]
[9] Han T W, He P F 2010 Acta Phys. Sin. 59 3408 (in Chinese)
[10] Ryzhii M, Ryzhii V 2007 Jpn. J. Appl. Phys. 46 L151
[11] Ryzhii V, Ryzhii M, Satou A, Otsuji T, Dubinov A A, Ya Aleshkin V 2007 J. Appl. Phys. 106 0908
[12] Ryzhii M, Ryzhii V, Otsuji T, Mitin V, Shur M S 2010 Phys. Rev. B 82 075419
[13] Neugebauer P, Orlita M, Faugeras C, Barra A L, PotemskiM2009 Phys. Rev. Lett. 103 136403
[14] Orlita M, Potemski M 2010 Semicond. Sci. Technol. 25 063001
[15] Miller D L, Kubista K D, Rutter G M, Ruan M, deHeerWA, First P N, Stroscio J A 2009 Science 324 924
[16] Sprinkle M, Siegel D, Hu Y, Hicks J, Tejeda A, TalebIbrahimi A, Le F`evre P, Bertran F, Vizzini S, Enriquez H, Chiang S, Soukiassian P, Berger C, de HeerWA, Lanzara A, Conrad E H 2009 Phys. Rev. Lett. 103 226803
[17] Ryzhii V, Ryzhii M, Satou A, Otsuji T, Dubinov A A, Ya Aleshkin V 2009 J. Appl. Phys. 106 084507
[18] Ryzhii V, Dubinov A A, Otsuji T, Mitin V, Shur M S 2010 J.Appl. Phys. 107 054505
[19] Ryzhii V, Ryzhii M, Mitin V, Otsuji T 2010 J. Appl. Phys. 107 054512
[20] Zheng Y, Ando T 2002 Phys. Rev. B 65 245420
[21] Gusynin V P, Sharapov S G 2006 Phys. Rev. B 73 245411
[22] Falkovsky L A 2006 Phys. Rev. B 75 033409
[23] Falkovsky L A, Varlamov A A 2007 EPJ B 56 4
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[1] Zhang Y, Tan Y W, Stormer H L, Kim P. 2005 Nature (London) 438 201
[2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Dubonos S V, Firsov A A 2005 Nature (London) 438 197
[3] Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620
[4] Geim A K, Novoselov K S 2007 Nat. Mater. 6 183
[5] Ryzhii V Ryzhii M, Otsuji T 2007 J. Appl. Phys. 101 083114
[6] Kang C Y, Tang J, Li L M 2011 Acta Phys. Sin. 047302 (in Chinese) [康朝阳, 唐军, 李利民 2011 {物理学报 60 047302]
[7] Jin Z F, Tong G P, Jiang Y J 2009 Acta Phys. Sin. 58 8537 (in Chinese) [金子飞, 童国平, 蒋永进 2009 {物理学报 58 8537]
[8] Pan H Z, Xu M, Chen L 2010 Acta Phys. Sin. 59 6443 (in Chinese) [潘洪哲, 徐明, 陈丽 2010 {物理学报 59 6443]
[9] Han T W, He P F 2010 Acta Phys. Sin. 59 3408 (in Chinese)
[10] Ryzhii M, Ryzhii V 2007 Jpn. J. Appl. Phys. 46 L151
[11] Ryzhii V, Ryzhii M, Satou A, Otsuji T, Dubinov A A, Ya Aleshkin V 2007 J. Appl. Phys. 106 0908
[12] Ryzhii M, Ryzhii V, Otsuji T, Mitin V, Shur M S 2010 Phys. Rev. B 82 075419
[13] Neugebauer P, Orlita M, Faugeras C, Barra A L, PotemskiM2009 Phys. Rev. Lett. 103 136403
[14] Orlita M, Potemski M 2010 Semicond. Sci. Technol. 25 063001
[15] Miller D L, Kubista K D, Rutter G M, Ruan M, deHeerWA, First P N, Stroscio J A 2009 Science 324 924
[16] Sprinkle M, Siegel D, Hu Y, Hicks J, Tejeda A, TalebIbrahimi A, Le F`evre P, Bertran F, Vizzini S, Enriquez H, Chiang S, Soukiassian P, Berger C, de HeerWA, Lanzara A, Conrad E H 2009 Phys. Rev. Lett. 103 226803
[17] Ryzhii V, Ryzhii M, Satou A, Otsuji T, Dubinov A A, Ya Aleshkin V 2009 J. Appl. Phys. 106 084507
[18] Ryzhii V, Dubinov A A, Otsuji T, Mitin V, Shur M S 2010 J.Appl. Phys. 107 054505
[19] Ryzhii V, Ryzhii M, Mitin V, Otsuji T 2010 J. Appl. Phys. 107 054512
[20] Zheng Y, Ando T 2002 Phys. Rev. B 65 245420
[21] Gusynin V P, Sharapov S G 2006 Phys. Rev. B 73 245411
[22] Falkovsky L A 2006 Phys. Rev. B 75 033409
[23] Falkovsky L A, Varlamov A A 2007 EPJ B 56 4
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