Hamiltonian of a many-electron system with single-electron and electron-pair states in a two-dimensional periodic potential

TL;DR

This paper develops a Hamiltonian model for a 2D many-electron system including single electrons and metastable electron pairs, comparing scenarios where the band is conduction or valence, and analyzing interactions and stabilization mechanisms.

Contribution

It introduces a Hamiltonian incorporating electron and electron-pair states in a 2D periodic potential, linking to existing models and highlighting the role of holes in stabilizing electron pairs.

Findings

Hamiltonian includes electron-electron and electron-pair interactions.

Comparison with boson-fermion mixture models.

Holes are crucial for stabilizing electron-pair states.

Abstract

Based on the metastable electron-pair energy band in a two-dimensional (2D) periodic potential obtained previously by Hai and Castelano [J. Phys.: Condens. Matter 26, 115502 (2014)], we present in this work a Hamiltonian of many electrons consisting of single electrons and electron pairs in the 2D system. The electron-pair states are metastable of energies higher than those of the single-electron states at low electron density. We assume two different scenarios for the single-electron band. When it is considered as the lowest conduction band of a crystal, we compare the obtained Hamiltonian with the phenomenological model Hamiltonian of a boson-fermion mixture proposed by Friedberg and Lee [Phys. Rev. B 40, 6745 (1989)]. Single-electron-electron-pair and electron-pair-electron-pair interaction terms appear in our Hamiltonian and the interaction potentials can be determined from the electron-electron Coulomb interactions. When we consider the single-electron band as the highest valence band of a crystal, we show that holes in this valence band are important for stabilization of the electron-pair states in the system.