2006/03/31 by Yasumasa Hasegawa, Mahito Kohmoto · 4 citations
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.74.155415
published as Phys. Rev. B 74, 155415 (2006) · 4 pages, 10 figures
arxiv created 2006/06/21 · openalex publication_date 2006/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, an unusual integer quantum Hall effect was observed in graphene in which the Hall conductivity is quantized as \ensuremathσxy=(\ifmmode±\else\textpm\fi2,\ifmmode±\else\textpm\fi6,\ifmmode±\else\textpm\fi10,…)\ifmmode×\else\texttimes\fie2∕h, where e is the electron charge and h is the Planck constant. To explain this we consider the energy structure as a function of magnetic field (the Hofstadter butterfly diagram) on the honeycomb lattice and the Streda formula for Hall conductivity. The quantized Hall conductivities are identified as the topological TKNN integers [D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982); M. Kohmoto, Ann. Phys. (N.Y.) 160, 343 (1985)]. They are odd integers \ifmmode±\else\textpm\fi1,\ifmmode±\else\textpm\fi3,\ifmmode±\else\textpm\fi5,…\ifmmode×\else\texttimes\fi2 (spin degrees of freedom) when a uniform magnetic field is as high as 30\phantom\rule0.3em0exT for example. The gaps corresponding to even integers, \ifmmode±\else\textpm\fi2,\ifmmode±\else\textpm\fi4,\ifmmode±\else\textpm\fi6,… are too small to be observed, but when the system is anisotropic, which is described by the generalized honeycomb lattice, and/or in an extremely strong magnetic field, quantization in even integers takes place as well. We also compare the results with those for the square lattice in an extremely strong magnetic field.