Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices

TL;DR

This paper provides an exact analysis of non-equilibrium quantum transport in quantum wires and fractional quantum Hall devices, revealing universal scaling functions, a critical conductance maximum, and a duality between tunneling regimes.

Contribution

It introduces an exact calculation of current-voltage characteristics and conductance in a Luttinger liquid, including a universal scaling form and a duality between strong and weak backscattering regimes.

Findings

Conductance exhibits a universal scaling with voltage and temperature.

A pronounced maximum in differential conductance occurs at a specific voltage-to-temperature ratio.

An exact duality relates electron and quasiparticle tunneling regimes.

Abstract

We have recently calculated exact non-equilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact $I(V)$ characteristic and conductance out of equilibrium as a function of driving voltage $V$ and temperature $T$. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and $V/T$. The differential-conductance curve as a function of the interaction strength broadens significantly as $V/T$ is increased, and develops a pronounced maximum at a (universal) critical value $(e V/k_B T)=7.18868...$. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.