Numerical study of electronic structure under uniform magnetic field and quantized Hall conductance for multi-band tight-binding models

The electronic structure of periodic lattice under uniform magnetic field was studied numerically for multi-band tight-binding models with non-orthogonal basis sets. When magnetic translational symmetry is fully taken into account, computational time can be greatly reduced. Quantized Hall conductance was evaluated by robust multi-band formulation of Chern number. We found that calculated quantized Hall conductance coincides with the semi-classical results. Discontinuous jumps of Hall conductance occur at van-Hove singularities and correspond to mod q ambiguity of the Diophantine equation of Chern number.