Why holes are not like electrons: A microscopic analysis of the differences between holes and electrons in condensed matter

Abstract

We give a detailed microscopic analysis of why holes are different from electrons in condensed matter. Starting from a single atom with zero, one and two electrons, we show that the spectral functions for electrons and for holes are qualitatively different because of electron-electron interactions. The quantitative importance of this difference increases as the charge of the nucleus decreases. Extrapolating our atomic analysis to the solid, we discuss the expected differences in the single particle spectral function and in frequency dependent transport properties for solids with nearly empty and nearly full electronic energy bands. We discuss the expected dependence of these quantities on doping, and the physics of superconductivity that results. We also discuss how these features of the atomic physics can be modeled by a variety of model Hamiltonians.