Sample Shape and Boundary Dependence of Measured Transverse Thermal Properties

TL;DR

This paper investigates how sample shape and boundary conditions influence the accuracy of measured transverse thermal properties, proposing simulation-based corrections and a contactless optical method for improved reliability in thermal Hall measurements.

Contribution

It introduces a simulation approach to quantify geometric effects on thermal Hall measurements and proposes a contactless optical technique to mitigate contact misalignment issues.

Findings

Measured $D_{xy}$ can vary significantly with sample geometry.

Rectangular samples improve measurement reliability.

Contactless optical method reduces misalignment errors.

Abstract

Despite increased interest in thermal Hall measurements for the analysis of insulating quantum materials, there remains large uncertainty in such measurements due to contact misalignment. In this paper we propose that sample geometry and uncertain boundary conditions may account for uncertainty in the measurement of $D_{xy}$ or $\kappa_{xy}$ as well. By running simple simulations in an open source finite-element solver, we demonstrate that measured $D_{xy}$ in a thermal Hall bar can be changed by a factor of order unity in samples with similar width and length. This geometric corrective factor depends on the distinction between uniform heat flow and constant temperature boundary couplings to a bath. Sample geometry and boundary conditions can be accounted for through simulation or by using rectangular samples to make thermal Hall measurements more reliable and reproducible when the amplitude of $\kappa_{xy}$ is important. Finally, we propose a contactless optical method for measuring $D_{xy}$ which is insensitive to the longitudinal diffusivity pollution caused by contact misalignment.