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

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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this study, Bloch's theorem was applied to investigate the interaction between a pair of electrons in periodic one-dimensional and two-dimensional lattices with intra-site and nearest neighbor inter-site interactions. The electronic structures were classified into binding bands and unbinding continuum states, with the presence of binding bands in both interaction types. These binding bands were found to be separated from the unbinding continuum states by gaps, depending on the nature of the interaction potential.