The polaronic effect of a metal layer on variable range hopping

TL;DR

This paper studies how a metal layer influences variable range hopping in a 2D electron-glass, revealing a dynamical polaronic effect that suppresses conductivity over a broad temperature range, beyond static screening effects.

Contribution

It introduces the dynamical polaronic effect of a metal layer on VRH conductivity, highlighting a wider temperature suppression compared to static effects.

Findings

Dynamical suppression of phonon-assisted hopping due to polaronic phenomena.

Static screening increases low-temperature conductivity.

Wider temperature range of conductivity suppression than static effects.

Abstract

We investigate the effect of a metal plate on the variable range hopping (VRH) conductivity of a two dimensional electron-glass (EG) system. The VRH conductivity is known to have a stretched exponential dependence on temperature, with an exponent $p$ that depends on the shape of the EG's single particle density of states (DOS). For constant DOS $p=1/3$ and for linear DOS $p=1/2$, also known as Mott's and Efros-Shklovskii's VRH respectively. The presence of the plate causes two effects on the EG system, static and dynamic. The well known static effect accounts for the additional screening of the Coulomb repulsion in the EG and for the partial filling of the Coulomb gap in the DOS. This in turn causes an increase of the conductivity at very low temperatures. Here we investigate the complementary dynamical effect, which is related to the polaronic phenomena. Our main result is the dynamical suppression of the standard phonon assisted hopping and, thus, suppression of the conductivity in a much wider range of temperatures as compared to the low temperature static effect. The relation to experiments is discussed.