Coulomb interaction in graphene: Relaxation rates and transport

Physical Review B - Condensed Matter and Materials Physics

Volumn 83, Issue 15, 2011, Pages

  Schutt M ^a   Ostrovsky, P M ^a,b   Gornyi, I V ^a,c   Mirlin, A D ^a,d  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^c IOFFE INSTITUTE   (Russian Federation)

^d PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79961092773     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.83.155441     Document Type: Article

References (97)

1. A. K. Geim and K. S. Novoselov, Nat. Mater. 1476-1122 10.1038/nmat1849 6, 183 (2007). (Pubitemid 46353764)
2. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.109 81, 109 (2009).
3. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science SCIEAS 0036-8075 10.1126/science.1102896 306, 666 (2004). (Pubitemid 39440910)
4. K. S. Novoselov, D. Jiang, T. Booth, V. V. Khotkevich, S. M. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0502848102 102, 10451 (2005). (Pubitemid 41061574)
5. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature (London) NATUAS 0028-0836 10.1038/nature04233 438, 197 (2005). (Pubitemid 41599867)
6. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London) NATUAS 0028-0836 10.1038/nature04235 438, 201 (2005); (Pubitemid 41599868)
7. Y.-W. Tan, Y. Zhang, H. L. Stormer, and P. Kim, Eur. Phys. J. Special Topics NATUAS 1951-6355 10.1140/epjst/e2007-00221-9 148, 15 (2007).
8. M. I. Katsnelson, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2006- 00203-1 51, 157 (2006). (Pubitemid 43876887)
9. J. Tworzydlo, B. Trauzettel, M. Titov, A. Rycerz, and C. W. J. Beenakker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.246802 96, 246802 (2006); (Pubitemid 43927090)
10. C. W. J. Beenakker, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys. 80.1337 80, 1337 (2008).
11. S. Ryu, C. Mudry, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B RMPHAT 1098-0121 10.1103/PhysRevB.75.205344 75, 205344 (2007).
12. F. Miao, S. Wijeratne, Y. Zhang, U. C. Coskun, W. Bao, and C. N. Lau, Science SCIEAS 0036-8075 10.1126/science.1144359 317, 1530 (2007). (Pubitemid 47417429)
13. R. Danneau, F. Wu, M. F. Craciun, S. Russo, M. Y. Tomi, J. Salmilehto, A. F. Morpurgo, and P. J. Hakonen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.196802 100, 196802 (2008). (Pubitemid 351692667)
14. M. Titov, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/79/17004 79, 17004 (2007).
15. A. Schuessler, P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B EULEEJ 1098-0121 10.1103/PhysRevB.79.075405 79, 075405 (2009).
16. M. Titov, P. M. Ostrovsky, I. V. Gornyi, A. Schuessler, and A. D. Mirlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.076802 104, 076802 (2010).
17. J. H. Bardarson, J. Tworzydło, P. W. Brouwer, and C. W. J. Beenakker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.106801 99, 106801 (2007); (Pubitemid 47501106)
18. K. Nomura, M. Koshino, and S. Ryu, Phys. Rev. Lett. 0031-9007 PRLTAO 10.1103/PhysRevLett.99.146806 99, 146806 (2007); (Pubitemid 47549446)
19. P. San-Jose, E. Prada, and D. S. Golubev, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.195445 76, 195445 (2007);
20. C. H. Lewenkopf, E. R. Mucciolo, and A. H. Castro Neto, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.77.081410 77, 081410 (R) (2008);
21. J. Tworzydło, C. W. Groth, and C. W. J. Beenakker, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.78.235438 78, 235438 (2008).
22. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.256801 98, 256801 (2007); (Pubitemid 47139947)
23. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Eur. Phys. J. Spec. Top. PRLTAO 1951-6355 10.1140/epjst/e2007-00226-4 148, 63 (2007).
24. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.74.235443 74, 235443 (2006).
25. P. M. Ostrovsky, M. Titov, S. Bera, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.266803 105, 266803 (2010).
26. T. Stauber, N. M. R. Peres, and F. Guinea, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.205423 76, 205423 (2007).
27. T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.75.074716 75, 074716 (2006).
28. K. Nomura and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.076602 98, 076602 (2007).
29. A. F. Morpurgo and F. Guinea, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.196804 97, 196804 (2006). (Pubitemid 44730441)
30. R. V. Gorbachev, F. V. Tikhonenko, A. S. Mayorov, D. W. Horsell, and A. K. Savchenko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.176805 98, 176805 (2007); (Pubitemid 46676955)
31. F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev, and A. K. Savchenko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.056802 100, 056802 (2008); (Pubitemid 351220704)
32. D. W. Horsell, A. K. Savchenko, F. V. Tikhonenko, K. Kechedzhi, I. V. Lerner, and V. I. Fal'ko, Solid State Commun. SSCOA4 0038-1098 10.1016/j.ssc.2009.02.058 149, 1041 (2009).
33. F. V. Tikhonenko, A. A. Kozikov, A. K. Savchenko, and R. V. Gorbachev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.226801 103, 226801 (2009).
34. E. McCann, K. Kechedzhi, V. I. Fal'ko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.146805 97, 146805 (2006); (Pubitemid 44522385)
35. K. Kechedzhi, V. I. Fal'ko, E. McCann, and B. L. Altshuler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.176806 98, 176806 (2007). (Pubitemid 46676954)
36. V. V. Cheianov and V. I. Falko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.226801 97, 226801 (2006). (Pubitemid 44826903)
37. A. A. Kozikov, A. K. Savchenko, B. N. Narozhny, and A. V. Shytov, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.82.075424 82, 075424 (2010).
38. X. Du, I. Skachko, A. Barker, and E. Y. Andrei, Nat. Nanotechnol. PRLTAO 1748-3387 10.1038/nnano.2008.199 3, 491 (2008);
39. X. Du, I. Skachko, A. Barker, and E. Y. Andrei, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979208050334 22, 4579 (2008).
40. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, Solid State Commun. SSCOA4 0038-1098 10.1016/j.ssc.2008.02.024 146, 351 (2008).
41. X. Du, I. Skachko, F. Duerr, A. Luican, and E. Y. Andrei, Nature NATUAS 0028-0836 10.1038/nature08522 462, 192 (2009).
42. K. I. Bolotin, F. Ghahari, M. D. Shulman, H. L. Stormer, and P. Kim, Nature (London) NATUAS 0028-0836 10.1038/nature08582 462, 196 (2009).
43. I. Skachko, X. Du, F. Duerr, A. Luican, D. A. Abanin, L. S. Levitov, and E. Y. Andrei, Phil. Trans. R. Soc. A 1364-503X 10.1098/rsta.2010.0226 368, 5403 (2010);
44. D. A. Abanin, I. Skachko, X. Du, E. Y. Andrei, and L. S. Levitov, Phys. Rev. B NATUAS 1098-0121 10.1103/PhysRevB.81.115410 81, 115410 (2010).
45. B. L. Altshuler and A. G. Aronov, in Electron-Electron Interactions in Disordered Systems, edited by, A. L. Efros, and, M. Pollak, (Elsevier, Amsterdam, 1985), p. 1.
46. J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, Science SCIEAS 0036-8075 10.1126/science.1190920 330, 805 (2010).
47. J. Gonzalez, F. Guinea, and M. A. H. Vozmediano, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90410-3 424, 596 (1994).
48. D. T. Son, Phys. Rev. B NUPBBO 1098-0121 10.1103/PhysRevB.75.235423 75, 235423 (2007).
49. J. Ye and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5409 80, 5409 (1998).
50. J. Ye, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.60.8290 60, 8290 (1999).
51. T. Stauber, F. Guinea, and M. A. H. Vozmediano, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.71.041406 71, 041406 (R) (2005). (Pubitemid 40418052)
52. D. E. Sheehy and J. Schmalian, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.226803 99, 226803 (2007). (Pubitemid 350198425)
53. M. S. Foster and I. L. Aleiner, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.77.195413 77, 195413 (2008).
54. M. S. Foster and A. W. W. Ludwig, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.73.155104 73, 155104 (2006). (Pubitemid 43516772)
55. D. V. Khveshchenko and H. Leal, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.03.020 687, 323 (2004); (Pubitemid 38570557)
56. D. V. Khveshchenko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.246802 87, 246802 (2001);
57. D. V. Khveshchenko, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/21/7/075303 21, 075303 (2009).
58. E. V. Gorbar, V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. B JCOMEL 1098-0121 10.1103/PhysRevB.66.045108 66, 045108 (2002).
59. I. F. Herbut, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 146401 97, 146401 (2006); (Pubitemid 44498323)
60. O. Vafek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.216401 98, 216401 (2007). (Pubitemid 47139649)
61. I. L. Aleiner, D. E. Kharzeev, and A. M. Tsvelik, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.195415 76, 195415 (2007).
62. S. J. Hands and C. G. Strouthos, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.78.165423 78, 165423 (2008).
63. J. E. Drut and T. A. Lähde, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.026802 102, 026802 (2009);
64. J. E. Drut and T. A. Lähde, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.79.165425 79, 165425 (2009).
65. G.-Z. Liu, W. Li, and G. Cheng, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.79.205429 79, 205429 (2009).
66. L. Sheng, D. N. Sheng, F. D. M. Haldane, and L. Balents, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.196802 99, 196802 (2007). (Pubitemid 350074473)
67. K. Nomura and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.256602 96, 256602 (2006). (Pubitemid 43974586)
68. D. A. Abanin, P. A. Lee, and L. S. Levitov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.156801 98, 156801 (2007); (Pubitemid 46574377)
69. D. A. Abanin, K. S. Novoselov, U. Zeitler, P. A. Lee, A. K. Geim, and L. S. Levitov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.196806 98, 196806 (2007). (Pubitemid 47139515)
70. Z. Jiang, Y. Zhang, H. L. Stormer, and P. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.106802 99, 106802 (2007). (Pubitemid 47388591)
71. J. Gonzalez, F. Guinea, and M. A. H. Vozmediano, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3589 77, 3589 (1996).
72. E. H. Hwang, Ben Yu-Kuang Hu, and S. Das Sarma, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.115434 76, 115434 (2007).
73. A. B. Kashuba, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.78.085415 78, 085415 (2008).
74. L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.78.085416 78, 085416 (2008).
75. M. S. Foster and I. L. Aleiner, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.79.085415 79, 085415 (2009).
76. M. Müller and S. Sachdev, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.78.115419 78, 115419 (2008).
77. M. Müller, L. Fritz, and S. Sachdev, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.78.115406 78, 115406 (2008).
78. M. Müller, J. Schmalian, and L. Fritz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.025301 103, 025301 (2009).
79. M. Müller, L. Fritz, S. Sachdev, and J. Schmalian, in Advances in Theoretical Physics, edited by, V. Lebedev, and, M. Feigel'man, AIP Conf. Proc. No. 1134 (AIP, New York, 2009), p. 170.
80. A. Kamenev and A. Levchenko, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730902850504 58, 197 (2009).
81. J. Rammer and H. Smith, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.58.323 58, 323 (1986).
82. I. L. Aleiner and Ya. M. Blanter, Phys. Rev. B RMPHAT 1098-0121 10.1103/PhysRevB.65.115317 65, 115317 (2002).
83. I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Phys. Rev. B RMPHAT 1098-0121 10.1103/PhysRevB.75.085421 75, 085421 (2007).
84. A. G. Yashenkin, I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Phys. Rev. B RMPHAT 1098-0121 10.1103/PhysRevB.78.205407 78, 205407 (2008).
85. D. A. Bagrets, I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Semiconductors SMICES 1063-7826 10.1134/S1063782608080204 42, 994 (2008);
86. D. A. Bagrets, I. V. Gornyi, and D. G. Polyakov, Phys. Rev. B SMICES 1098-0121 10.1103/PhysRevB.80.113403 80, 113403 (2009);
87. S. Ngo Dinh, D. A. Bagrets, A. D. Mirlin, Phys. Rev. B SMICES 1098-0121 10.1103/PhysRevB.81.081306 81, 081306 (R) (2010).
88. D. B. Gutman, Y. Gefen, and A. D. Mirlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.126802 101, 126802 (2008);
89. D. B. Gutman, Y. Gefen, and A. D. Mirlin, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.80.045106 80, 045106 (2009).
90. B. N. Narozhny, G. Zala, and I. L. Aleiner, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.65.180202 65, 180202 (2002).
91. I. L. Aleiner, B. L. Altshuler, and M. E. Gershenson, Waves Random Media PRLTAO 1745-5030 10.1088/0959-7174/9/2/308 9, 201 (1999).
92. V. F. Gantmakher and Y. B. Levinson, Carrier Scattering in Metals and Semiconductors (North-Holland, Amsterdam, 1987).
93. B. N. Narozhny, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.153409 76, 153409 (2007).
94. Wang-Kong Tse, Ben Yu-Kuang Hu, and S. Das Sarma, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.081401 76, 081401 (R) (2007).
95. A. Schuessler, P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.82.085419 82, 085419 (2010).
96. A. D. Mirlin, F. Evers, I. V. Gornyi, and P. M. Ostrovsky, in 50 Years of Anderson Localization, edited by, E. Abrahams, (World Scientific, Singapore, 2010);
97. A. D. Mirlin, F. Evers, I. V. Gornyi, and P. M. Ostrovsky, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979210064526 24, 1577 (2010).