Non-linear $I(V)$ Characteristics of Luttinger Liquids and Gated Hall Bars

TL;DR

This paper calculates the non-linear current-voltage behavior and voltage fluctuations of disordered Luttinger liquids, revealing universal power laws at the superfluid-insulator transition and discussing implications for gated Hall bars.

Contribution

It introduces a perturbative formalism to analyze non-linear $I(V)$ characteristics and voltage fluctuations in disordered Luttinger liquids, highlighting universal behavior at the transition.

Findings

$I(V)$ follows a non-universal power law $V^{1/(2 ilde{g}-1)}$

Voltage fluctuations scale as $I^{4 ilde{g}-3}$

Universal power law behavior at the superfluid-insulator transition

Abstract

Non-linear current voltage characteristics of a disordered Luttinger liquid are calculated using a perturbative formalism. One finds non-universal power law characteristics of the form $I(V)\sim V^{1/(2\tilde{g}-1)}$ which is valid both in the superfluid phase when $I$ is small and also in the insulator phase when $I$ is large. Mesoscopic voltage fluctuations are also calculated. One finds $\Var(\Delta V) \sim I^{4\tilde{g}-3}$. Both the $I(V)$ characteristic and the voltage fluctuations exhibit universal power law behavior at the superfluid insulator transition where $\tilde{g}=\tot$. The possible application of these results to the non-linear transport properties of gated Hall bars is discussed.