Kinetic energy of electrons on a two-dimensional lattice with commensurate flux

Abstract

The kinetic energy of tight-binding electrons on a two-dimensional lattice with a perpendicular magnetic field has been studied using a recursion approach. For a fixed filling factor the energy is shown to exhibit several local minima as a function of flux. The minima correspond to the situation where the Fermi level lies in a gap. The absolute minimum corresponds to one flux quantum per particle.