Variable range hopping and quantum creep in one dimension

TL;DR

This paper investigates quantum creep and variable range hopping in a one-dimensional disordered system, revealing a crossover from quantum tunneling to linear response driven by electric field strength.

Contribution

It provides an explicit construction of metastable states and bounce instantons, demonstrating quantum creep and a crossover to variable range hopping behavior in 1D systems.

Findings

Quantum creep velocity follows an exponential form with electric field.

A sharp crossover at a critical electric field E* occurs.

The linear response at high fields aligns with variable range hopping theories.

Abstract

We study the quantum non linear response to an applied electric field $E$ of a one dimensional pinned charge density wave or Luttinger liquid in presence of disorder. From an explicit construction of low lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep $v = e^{- c/E^{1/2}}$ as well as a sharp crossover at $E=E^*$ towards a linear response form consistent with variable range hopping arguments, but dependent only on electronic degrees of freedom.