▎ 摘　　要

Recently, an unusual integer quantum Hall effect was observed in graphene in which the Hall conductivity is quantized as sigma(xy)=(+/- 2,+/- 6,+/- 10,...)xe(2)/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 +/- 1,+/- 3,+/- 5,...x2 (spin degrees of freedom) when a uniform magnetic field is as high as 30 T for example. The gaps corresponding to even integers, +/- 2,+/- 4,+/- 6,... 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.