Direct Determination of the Topological Thermal Conductance via Local Power Measurement

TL;DR

This paper introduces a novel local power measurement method to directly determine the topological thermal Hall conductance in two-dimensional topological insulators, providing more accurate insights into their topological order.

Contribution

The authors develop a new local power measurement technique that accurately measures topological thermal Hall conductance, overcoming limitations of previous two-terminal methods.

Findings

Measured $ u=2/3$ state with $oxed{ ext{negligible } ext{kappa}_{xy}}$

Revealed non-universal values in two-terminal measurements due to thermal equilibration

Studied power fluctuations in out-of-equilibrium edge modes

Abstract

Thermal conductance measurements, sensitive to charge and chargeless energy flow, are evolving as an essential measurement technique in Condensed Matter Physics. For two-dimensional topological insulators, the measurements of the thermal Hall conductance, $\kappa_{xy}T$, and the longitudinal one $\kappa_{xx}T$, are crucial for the understanding of their underlying topological order. Such measurements are thus far lacking, even in the extensively studied quantum Hall effect (QHE) regime. Here, we report a new local power measurement technique that reveals the topological thermal Hall conductance (not the ubiquitous two-terminal one). For example, we find $\kappa_{xy}\sim0$ of the challenging $\nu=2/3$ particle-hole conjugated state. This is in contrast to the two-terminal measurement, which provides a non-universal value that depends on the extent of thermal equilibration between the counter-propagating edge modes. Moreover, we use this technique to study the power carried by the current fluctuations in a partitioned edge mode with an out-of-equilibrium distribution.