Coulomb gap in the one-particle density of states in three-dimensional systems with localized electrons

TL;DR

This paper investigates the Coulomb gap in the density of states of 3D localized electron systems, revealing a crossover from quadratic to exponential depletion influenced by excitonic interactions, explaining previous simulation results.

Contribution

It demonstrates that excitonic interactions can delay the exponential depletion of the Coulomb gap in 3D systems, refining the understanding of the Coulomb gap behavior.

Findings

Intermediate energy range shows strong compensation of depletion.

Crossover from quadratic to exponential behavior is retarded.

Exponential depletion is less observable in simulations due to this effect.

Abstract

The one-particle density of states (1P-DOS) in a system with localized electron states vanishes at the Fermi level due to the Coulomb interaction between electrons. Derivation of the Coulomb gap uses stability criteria of the ground state. The simplest criterion is based on the excitonic interaction of an electron and a hole and leads to a quadratic 1P-DOS in the three-dimensional (3D) case. In 3D, higher stability criteria, including two or more electrons, were predicted to exponentially deplete the 1P-DOS at energies close enough to the Fermi level. In this paper we show that there is a range of intermediate energies where this depletion is strongly compensated by the excitonic interaction between single-particle excitations, so that the crossover from quadratic to exponential behavior of the 1P-DOS is retarded. This is one of the reasons why such exponential depletion was never seen in computer simulations.