Coulomb gap in one-dimensional disordered electronic systems

TL;DR

This paper investigates the effects of long-range Coulomb interactions and disorder on a one-dimensional system of spinless electrons, revealing how these factors influence localization and the density of states.

Contribution

It provides a combined analytical approach using bosonization, replica trick, and renormalization group to analyze Coulomb gap formation in disordered 1D electron systems.

Findings

Localization length depends on disorder and interactions.

Density of states varies with energy relative to localization length.

Long-range Coulomb interactions significantly reduce the TLL interaction parameter.

Abstract

We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb interaction (LRCI) and a random chemical potential at each site. We first present a Tomonaga-Luttinger liquid (TLL) description of the system. We use the bosonization technique followed by the replica trick to average over the quenched randomness. An expression for the localization length of the system is then obtained using the renormalization group method and also a physical argument. We then find the density of states for different values of the energy; we get different expressions depending on whether the energy is larger than or smaller than the inverse of the localization length. We work in the limit of weak disorder where the localization length is very large; at that length scale, the LRCI has the effect of reducing the interaction parameter K of the TLL to a value much smaller than the noninteracting value of unity.