Nonlocal thermoelectric detection of interaction and correlations in edge states

TL;DR

This paper proposes using nonlocal thermoelectric effects in quantum Hall edge states as a direct measure of electron interactions, correlations, and thermalization processes in nonequilibrium quantum conductors.

Contribution

It introduces a novel thermoelectric detection method for interactions and correlations in quantum edge states, analyzing energy exchange and thermalization through a controllable setup.

Findings

Nonlocal Seebeck response indicates interaction strength.

Universal energy equilibration length scale identified.

Thermoelectric measurements reveal thermalization and correlations.

Abstract

We investigate nonequilibrium effects in the transport of interacting electrons in quantum conductors, proposing the nonlocal thermoelectric response as a direct indicator of the presence of interactions, nonthermal states and the effect of correlations. This is done by assuming a quantum Hall setup where two channels (connected to reservoirs at different temperatures) co-propagate for a finite distance, such that a thermoelectrical response is only expected if the electron-electron interaction mediates heat exchange between the channels. This way, the nonlocal Seebeck response measures the interaction strength. Considering zero-range interactions, we solve the charge and energy currents and noises of a non-equilibrium integrable interacting system, determining the universal interaction-dependent length scale of energy equilibration. Further, a setup with two controllable quantum point contacts allows thermoelectricity to monitor the interacting system thermalisation as well as the fundamental role of cross-correlations in the heat exchange at intermediate length scales.