Quantum criticality and minimal conductivity in graphene with long-range disorder

Physical Review Letters

Volumn 98, Issue 25, 2007, Pages

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

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^c UNIVERSITY OF KARLSRUHE   (Germany)

^d IOFFE INSTITUTE   (Russian Federation)

^e PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC CONDUCTIVITY; GRAPHITE; HALL EFFECT; MATHEMATICAL MODELS;

FIELD THEORY; GRAPHENE; QUANTUM CRITICALITY; TIME REVERSAL SYMMETRY;

QUANTUM THEORY;

EID: 34547372352     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.98.256801     Document Type: Article

References (45)

1. K.S. Novoselov, Science 306, 666 (2004). SCIEAS 0036-8075 10.1126/science.1102896
2. K.S. Novoselov, Nature (London) NATUAS 0028-0836 438, 197 (2005); 10.1038/nature04233
3. K.S. Novoselov Nature Phys. 2, 177 (2006); 1745-2481 10.1038/nphys245
4. Y. Zhang, Nature (London) NATUAS 0028-0836 438, 201 (2005); 10.1038/nature04235
5. Y. Zhang Phys. Rev. Lett. 96, 136806 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.96.136806
6. S.V. Morozov, Phys. Rev. Lett. 97, 016801 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.016801
7. E. McCann, Phys. Rev. Lett. 97, 146805 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.146805
8. I.L. Aleiner and K.B. Efetov, Phys. Rev. Lett. 97, 236801 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.97.236801
9. A. Altland, Phys. Rev. Lett. 97, 236802 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.236802
10. P.M. Ostrovsky, I.V. Gornyi, and A.D. Mirlin, Phys. Rev. B PRBMDO 0163-1829 74, 235443 (2006). 10.1103/PhysRevB.74.235443
11. S. Ryu, arXiv:cond-mat/0610598.
12. A.F. Morpurgo and F. Guinea, Phys. Rev. Lett. 97, 196804 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.97.196804
13. J.C. Meyer, Nature (London) NATUAS 0028-0836 446, 60 (2007). 10.1038/nature05545
14. K. Nomura and A.H. MacDonald, Phys. Rev. Lett. 98, 076602 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.076602
15. A. Rycerz, J. Tworzydlo, and C.W.J. Beenakker, arXiv:cond-mat/0612446.
16. A.W.W. Ludwig, Phys. Rev. B PRBMDO 0163-1829 50, 7526 (1994). 10.1103/PhysRevB.50.7526
17. A.A. Nersesyan, A.M. Tsvelik, and F. Wenger, Nucl. Phys. B NUPBBO 0550-3213 438, 561 (1995). 10.1016/0550-3213(95)00002-A
18. K.B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, England, 1996).
19. M.V. Berry and R.J. Mondragon, Proc. R. Soc. A PRLAAZ 0080-4630 412, 53 (1987). 10.1098/rspa.1987.0080
20. F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.61.2015
21. An alternative route from the Dirac anomaly to a topological term employs non-Abelian bosonization; see M. Bocquet, D. Serban, and M.R. Zirnbauer, Nucl. Phys. NUPBBO 0550-3213 B578, 628 (2000); 10.1016/S0550-3213(00)00208-X
22. A. Altland, B.D. Simons, and M.R. Zirnbauer, Phys. Rep. 359, 283 (2002). This method was used in (b) to derive the σ-model for graphene with node mixing (without the θ=π topological term). PRPLCM 0370-1573 10.1016/S0370-1573(01)00065-5
23. K. Fujikawa, Phys. Rev. D 21, 2848 (1980). PRVDAQ 0556-2821 10.1103/PhysRevD.21.2848
24. A.M.M. Pruisken, Nucl. Phys. NUPBBO 0550-3213 B235, 277 (1984); 10.1016/0550-3213(84)90101-9
25. A.M.M. Pruisken in The Quantum Hall Effect edited by, R.E. Prange, and, S.M. Girvin, (Springer, New York, 1987), p. 117.
26. Y. Huo, Phys. Rev. Lett. 70, 481 (1993); PRLTAO 0031-9007 10.1103/PhysRevLett.70.481
27. B.M. Gammel and W. Brenig, Phys. Rev. Lett. 73, 3286 (1994); PRLTAO 0031-9007 10.1103/PhysRevLett.73.3286
28. Z. Wang, Phys. Rev. Lett. 77, 4426 (1996); PRLTAO 0031-9007 10.1103/PhysRevLett.77.4426
29. S. Cho and M.P.A. Fisher, Phys. Rev. B PRBMDO 0163-1829 55, 1637 (1997); 10.1103/PhysRevB.55.1637
30. L. Schweitzer and P. Markoš, Phys. Rev. Lett. 95, 256805 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.256805
31. D.B. Fuchs and O.Ya. Viro, Topology II, edited by, V.A. Rokhlin, and, S.P. Novikov, Encyclopaedia of Mathematical Sciences Vol. 24 (Springer, New York, 2004).
32. The possibility of the Z2 topological term in the 2D symplectic σ-model was emphasized in P. Fendley, Phys. Rev. B PRBMDO 0163-1829 63, 104429 (2001). 10.1103/PhysRevB.63.104429
33. P. Markoš and L. Schweitzer, J. Phys. A JPHAC5 0305-4470 39, 3221 (2006). 10.1088/0305-4470/39/13/003
34. C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802
35. L. Sheng, Phys. Rev. Lett. 95, 136602 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.136602
36. M. Onoda, Phys. Rev. Lett. 98, 076802 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.98.076802
37. B.A. Bernevig, Science 314, 1757 (2006). SCIEAS 0036-8075 10.1126/science.1133734
38. T. Ando and H. Suzuura, J. Phys. Soc. Jpn. 71, 2753 (2002); JUPSAU 0031-9015 10.1143/JPSJ.71.2753
39. Y. Takane, J. Phys. Soc. Jpn. 73, 1430 (2004); JUPSAU 0031-9015 10.1143/JPSJ.73.1430
40. H. Sakai and Y. Takane, J. Phys. Soc. Jpn. 75, 054711 (2006); JUPSAU 0031-9015 10.1143/JPSJ.75.054711
41. delocalization in the 1D symplectic class appeared earlier in M.R. Zirnbauer, Phys. Rev. Lett. 69, 1584 (1992); PRLTAO 0031-9007 10.1103/PhysRevLett.69.1584
42. A.D. Mirlin, A. Müller-Groeling, and M.R. Zirnbauer, Ann. Phys. (N.Y.) APNYA6 0003-4916 236, 325 (1994), but the distinction between an even and odd number of channels was not understood there.
43. S. Ryu, arXiv:cond-mat/0702529.
44. J.H. Bardarson, arXiv:0705.0886;
45. K. Nomura, arXiv:0705.1607.