Nonlinear conductance of long quantum wires at a conductance plateau transition: Where does the voltage drop?

TL;DR

This paper investigates the nonlinear conductance behavior of long, clean quantum wires with interactions near a conductance transition, revealing a universal conductance form and a surprising voltage drop near one wire end.

Contribution

It provides a detailed analysis of conductance near the quantum phase transition, including universal forms and the impact of three-particle scattering on voltage distribution.

Findings

Conductance near transition follows a universal form governed by temperature, bias, and gate voltage ratios.

Voltage predominantly drops near one end of the wire due to thermoelectric effects.

Analytic results agree with Boltzmann equation solutions including three-particle scattering.

Abstract

We calculate the linear and nonlinear conductance of spinless fermions in clean, long quantum wires where short-ranged interactions lead locally to equilibration. Close to the quantum phase transition where the conductance jumps from zero to one conductance quantum, the conductance obtains an universal form governed by the ratios of temperature, bias voltage and gate voltage. Asymptotic analytic results are compared to solutions of a Boltzmann equation which includes the effects of three-particle scattering. Surprisingly, we find that for long wires the voltage predominantly drops close to one end of the quantum wire due to a thermoelectric effect.