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Zero modes and the quantized Hall conductance of the two-dimensional lattice in a magnetic field

1989; American Physical Society; Volume: 39; Issue: 16 Linguagem: Inglês

10.1103/physrevb.39.11943

1095-3795

Mahito Kohmoto,

Physics of Superconductivity and Magnetism

Several properties of the tight-binding electrons in two dimensions with a uniform magnetic field perpendicular to the plane are discussed. The existence of zero-energy states is explicitly shown. The quantized value of the Hall conductance of each magnetic subband which is the Chern number of a certain fiber bundle on a two-torus is calculated. The holelike Hall coefficient can be explained by the quantum mechanics of negatively charged electrons.