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

Guo-Qiang Hai () and François Peeters

The European Physical Journal B: Condensed Matter and Complex Systems, 2015, vol. 88, issue 1, 1-5

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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Keywords: Solid State and Materials (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1140/epjb/e2014-50686-x

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