Emergence of massless Dirac fermions in graphene's Hofstadter butterfly at switches of the quantum hall phase connectivity

Physical Review Letters

Volumn 112, Issue 19, 2014, Pages

  Diez, M ^a   Dahlhaus, J P ^b   Wimmer, M ^c   Beenakker, C W J ^a  

^a UNIVERSITEIT LEIDEN   (Netherlands)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

PHOTONIC BAND GAP; QUANTUM THEORY;

CONICAL SINGULARITIES; CONNECTED COMPONENT; FRACTAL SPECTRUM; HEXAGONAL CRYSTALS; KLEIN TUNNELING; MASSLESS DIRAC FERMIONS; MODEL CALCULATIONS; QUANTUM NUMBERS;

GRAPHENE;

EID: 84901020661     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.196602     Document Type: Article

References (30)

1. D. Hofstadter, Phys. Rev. B 14, 2239 (1976). PLRBAQ 0556-2805 10.1103/PhysRevB.14.2239
2. D. Osadchy and J.E. Avron, J. Math. Phys. (N.Y.) 42, 5665 (2001). JMAPAQ 0022-2488 10.1063/1.1412464
3. L.A. Ponomarenko, R.V. Gorbachev, G.L. Yu, D.C. Elias, R. Jalil, A.A. Patel, A. Mishchenko, A.S. Mayorov, C.R. Woods, J.R. Wallbank, M. Mucha-Kruczynski, B.A. Piot, M. Potemski, I.V. Grigorieva, K.S. Novoselov, F. Guinea, V.I. Falko, and A.K. Geim, Nature (London) 497, 594 (2013). NATUAS 0028-0836 10.1038/nature12187
4. C.R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, K.L. Shepard, J. Hone, and P. Kim, Nature (London) 497, 598 (2013). NATUAS 0028-0836 10.1038/nature12186
5. B. Hunt, J.D. Sanchez-Yamagishi, A.F. Young, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero, and R.C. Ashoori, Science 340, 1427 (2013). SCIEAS 0036-8075 10.1126/science.1237240
6. R. Rammal, J. Phys. (Paris) 46, 1345 (1985). JOPQAG 0302-0738 10.1051/jphys:019850046080134500
7. J.-M. Hou, W.-X. Yang, and X.-J. Liu, Phys. Rev. A 79, 043621 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.79.043621
8. F. Gerbier and J. Dalibard, New J. Phys. 12, 033007 (2010). NJOPFM 1367-2630 10.1088/1367-2630/12/3/033007
9. P. Delplace and G. Montambaux, Phys. Rev. B 82, 035438 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.035438
10. J.-W. Rhim and K. Park, Phys. Rev. B 86, 235411 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.235411
11. B. Sachs, T.O. Wehling, M.I. Katsnelson, and A.I. Lichtenstein, Phys. Rev. B 84, 195414 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.195414
12. C. Ortix, L. Yang, and J. van den Brink, Phys. Rev. B 86, 081405(R) (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.081405
13. M. Yankowitz, J. Xue, D. Cormode, J.D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B.J. LeRoy, Nat. Phys. 8, 382 (2012). NPAHAX 1745-2473 10.1038/nphys2272
14. M. Kindermann, B. Uchoa, and D.L. Miller, Phys. Rev. B 86, 115415 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.115415
15. X. Chen, J.R. Wallbank, A.A. Patel, M. Mucha-Kruczyński, E. McCann, and V.I. Fal'ko, Phys. Rev. B 89, 075401 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.075401
16. J.R. Wallbank, A.A. Patel, M. Mucha-Kruczyński, A.K. Geim, and V.I. Fal'ko, Phys. Rev. B 87, 245408 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.245408
17. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, Rev. Mod. Phys. 81, 109 (2009). RMPHAT 0034-6861 10.1103/RevModPhys.81.109
18. M.I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, Cambridge, England, 2012).
19. The valley-isotropic Dirac Hamiltonian (1) acts on the spinor ((Equation presented), (Equation presented)) in valley (Equation presented) and ((Equation presented), (Equation presented)) in valley (Equation presented), where (Equation presented) and (Equation presented) are the wave amplitudes on the two triangular sublattices that form the hexagonal lattice of graphene.
20. Because the spin degree of freedom is not counted, the conductance quantum is (Equation presented) rather than (Equation presented).
21. D.S.L. Abergel, J.R. Wallbank, X. Chen, M. Mucha-Kruczyński, and V.I. Fal'ko, New J. Phys. 15, 123009 (2013). NJOPFM 1367-2630 10.1088/1367-2630/15/12/123009
22. C.W. Groth, M. Wimmer, A.R. Akhmerov, and X. Waintal, arXiv:1309.2926.
23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.112.196602 for details of the calculation.
24. C.W.J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.1337
25. M.I. Katsnelson, Eur. Phys. J. B 51, 157 (2006). EPJBFY 1434-6028 10.1140/epjb/e2006-00203-1 (Pubitemid 43876887)
26. J. Tworzydło, B. Trauzettel, M. Titov, A. Rycerz, and C.W.J. Beenakker, Phys. Rev. Lett. 96, 246802 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.246802 (Pubitemid 43927090)
27. M.I. Katsnelson, K.S. Novoselov, and A.K. Geim, Nat. Phys. 2, 620 (2006). NPAHAX 1745-2473 10.1038/nphys384 (Pubitemid 44328348)
28. V.V. Cheianov and V.I. Fal'ko, Phys. Rev. B, 74, 041403 (2006). PRBMDO 1098-0121 10.1103/PhysRevB.74.041403 (Pubitemid 44079267)
29. A.F. Young and P. Kim, Nat. Phys. 5, 222 (2009). NPAHAX 1745-2473 10.1038/nphys1198
30. C.R. Woods, L. Britnell, A. Eckmann, G.L. Yu, R.V. Gorbachev, A.V. Kretinin, J. Park, L.A. Ponomarenko, M.I. Katsnelson, Yu.N. Gornostyrev, K. Watanabe, T. Taniguchi, C. Casiraghi, A.K. Geim, and K.S. Novoselov, arXiv:1401.2637.