Local temperatures of strongly-correlated quantum dots out of equilibrium

TL;DR

This paper introduces a protocol for measuring local temperatures in out-of-equilibrium quantum dots, demonstrating that the measurements are consistent across different observables and regimes, aligning with traditional local equilibrium concepts.

Contribution

It proposes an experimentally feasible method to determine local temperatures in quantum dots out of equilibrium, validated by a highly accurate open quantum system approach.

Findings

Measured temperatures are insensitive to observable choice.

Results are consistent across noninteracting and Kondo regimes.

Temperatures align with traditional local equilibrium definitions.

Abstract

Probes that measure the local thermal properties of systems out of equilibrium are emerging as new tools in the study of nanoscale systems. One can then measure the temperature of a probe that is weakly coupled to a bias-driven system. By tuning the probe temperature so that the expectation value of some observable of the system is minimally perturbed, one obtains a parameter that measures its degree of local statistical excitation, and hence its local heating. However, one anticipates that different observables may lead to different temperatures and thus different local heating expectations. We propose an experimentally realizable protocol to measure such local temperatures and apply it to bias-driven quantum dots. By means of a highly accurate open quantum system approach, we show theoretically that the measured temperature is quite insensitive both to the choice of observable and to the probe-system coupling. In particular, even with observables that are distinct both physically and in their degree of locality, such as the local magnetic susceptibility of the quantum dot and the global spin-polarized current measured at the leads, the resulting local temperatures are quantitatively similar for quantum dots ranging from noninteracting to Kondo-correlated regimes, and are close to those obtained with the traditional "local equilibrium" definition.