Bloch's band structures of a pair of interacting electrons in simple one- and two-dimensional lattices

Abstract

We have applied the Bloch's theorem to a pair of interacting electrons in periodic simple one-dimensional lattice and two-dimensional square lattice with both intra-site and nearest neighbor inter-site interactions. The electronic structures can be classified as binding bands and unbinding continuum states of a pair of electrons. In addition to the usual intra-site binding band, we found the nearest-neighbor inter-site binding bands in both spin singlet and triplet states irrespective of interaction nature. The binding bands are either above or below the unbinding continuum states separated by gaps for a repulsive or attractive interaction potential.