Flat edge modes of graphene and of Z2 topological insulator

Nanoscale Research Letters

Volumn 6, Issue , 2011, Pages 1-6

  Imura, Ken Ichiro ^a,b   Mao, Shijun ^b,c   Yamakage, Ai ^b   Kuramoto, Yoshio ^b  

^a HIROSHIMA UNIVERSITY   (Japan)

^b TOHOKU UNIVERSITY   (Japan)

^c TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); ELECTRIC INSULATORS; GRAPHENE; SEMICONDUCTOR QUANTUM WELLS;

EDGE GEOMETRY; EDGE SPECTRA; FLAT BAND; GRAPHENE NANO-RIBBON; HGTE/CDTE; ZHANG MODEL; ZIGZAG EDGES;

TOPOLOGICAL INSULATORS;

EID: 84856042746     PISSN: 19317573     EISSN: 1556276X     Source Type: Journal    
DOI: 10.1186/1556-276X-6-358     Document Type: Review

References (24)

1. Wallace PR: The Band Theory of Graphite. Phys Rev 1947, 71(9):622-634.
2. Semenoff GW: Condensed-Matter Simulation of a Three-Dimensional Anomaly. Phys Rev Lett 1984, 53(26):2449-2452.
3. Geim AK, Novoselov KS: The rise of graphene. Nature Mater 2007, 6:183.
4. Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK: The electronic properties of graphene. Rev Mod Phys 2009, 81:109-162.
5. Ando T, Nakanishi T, Saito R: Berry's Phase and Absence of Back Scattering in Carbon Nanotubes. Journal of the Physical Society of Japan 1998, 67(8):2857-2862.
6. Katsnelson MI, Novoselov KS, Geim AK: Chiral tunnelling and the Klein paradox in graphene. Nature Phys 2006, 2:620.
7. Yamakage A, Imura KI, Cayssol J, Kuramoto Y: Spin-orbit effects in a graphene bipolar pn junction. EPL (Europhysics Letters) 2009, 87(4):47005.
8. Suzuura H, Ando T: Crossover from Symplectic to Orthogonal Class in a Two-Dimensional Honeycomb Lattice. Phys Rev Lett 2002, 89(26):266603.
9. Nomura K, Koshino M, Ryu S: Topological Delocalization of Two-Dimensional Massless Dirac Fermions. Phys Rev Lett 2007, 99(14):146806.
10. 2 topological insulator. Phys Rev B 2009, 80(8):085119.
11. Fujita M, Wakabayashi K, Nakada K, Kusakabe K: Peculiar Localized State at Zigzag Graphite Edge. Journal of the Physical Society of Japan 1996, 65(7):1920-1923.
12. Ryu S, Hatsugai Y: Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems. Phys Rev Lett 2002, 89(7):077002.
13. Yao W, Yang SA, Niu Q: Edge States in Graphene: From Gapped Flat-Band to Gapless Chiral Modes. Phys Rev Lett 2009, 102(9):096801.
14. Wakabayashi K, Takane Y, Sigrist M: Perfectly Conducting Channel and Universality Crossover in Disordered Graphene Nanoribbons. Phys Rev Lett 2007, 99(3):036601.
15. Datta S: Electronic transport in mesoscopic systems Cambridge Univ. Press; 1995.
16. Kane CL, Mele EJ: Quantum Spin Hall Effect in Graphene. Phys Rev Lett 2005, 95(22):226801.
17. 2 Topological Order and the Quantum Spin Hall Effect. Phys Rev Lett 2005, 95(14):146802.
18. Bernevig BA, Hughes TL, Zhang SC: Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells. Science 2006, 314:1757.
19. König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L, Qi XL, Zhang SC: Quantum Spin Hall Insulator State in HgTe Quantum Wells. Science 2007, 318:766.
20. Wen XG: Theory of the edge excitations in FQH effects. Int J Mod Phys B 1992, 6:1711.
21. 2 topological insulator: Reentrance and completely at spectrum. Phys Rev B 2010, 82(8):085118.
22. Fu L, Kane CL: Topological insulators with inversion symmetry. Phys Rev B 2007, 76(4):045302.
23. König M, Buhmann H, Molenkamp LW, Hughes T, Liu CX, Qi XL, Zhang SC: The Quantum Spin Hall Effect: Theory and Experiment. Journal of the Physical Society of Japan 2008, 77(3):031007.
24. Mao S, Kuramoto Y, Imura KI, Yamakage A: Analytic Theory of Edge Modes in Topological Insulators. Journal of the Physical Society of Japan 2010, 79(12):124709.