Coulomb gap and variable range hopping in a pinned Wigner crystal

TL;DR

This paper investigates how impurity pinning in a Wigner crystal creates localized states near the Fermi level, leading to a Coulomb gap and variable range hopping, with different impurity types affecting the density of states.

Contribution

It elucidates the mechanisms by which impurities induce localized states and Coulomb gaps in a pinned Wigner crystal, highlighting the roles of screening and dislocations.

Findings

Pinning creates localized states near the Fermi level.

Coulomb interactions lead to a soft Coulomb gap.

Variable range hopping occurs at low temperatures.

Abstract

It is shown that pinning of an electron Wigner crystal by a small concentration of charged impurities creates the finite density of charged localized states near the Fermi level. In the case of residual impurities in the spacer this density of states is related to nonlinear screening of a close acceptor by a Wigner crystal vacancy. On the other hand, intentional doping by a remote layer of donors is a source of a long range potential, which generates dislocations in Wigner crystal. Dislocations in turn create charged localized states near the Fermi level. In both cases Coulomb interaction of localized states leads to the soft Coulomb gap and ES variable range hopping at low enough temperatures.