Eur. Phys. J. B (2015) 88: 20
https://doi.org/10.1140/epjb/e2014-50686-x

Regular Article

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

¹ Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, SP, Brazil
² Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerpen, Belgium

^a e-mail: hai@ifsc.usp.br

Received: 7 October 2014
Received in final form: 11 November 2014
Published online: 14 January 2015

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.