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

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.