Departure from the Wiedemann-Franz Law in WP$_2$ Driven by Mismatch in $T$-square Resistivity Prefactors

TL;DR

This study investigates the breakdown of the Wiedemann-Franz law in WP$_2$ crystals at finite temperatures, revealing a mismatch driven by electron-electron scattering and suggesting a possible hydrodynamic electron regime.

Contribution

It demonstrates the temperature-dependent deviation from the Wiedemann-Franz law in WP$_2$, linked to a mismatch in resistivity prefactors caused by electron-electron interactions.

Findings

WF law holds at 2 K but deviates at higher temperatures

Large mismatch between Lorenz number and Sommerfeld value at 13 K

Electron-electron scattering causes the resistivity mismatch

Abstract

The Wiedemann-Franz (WF) law establishes a link between heat and charge transport due to electrons in solids. The extent of its validity in presence of inelastic scattering is a question raised in different contexts. We report on a study of the electrical, $\sigma$, and thermal, $\kappa$, conductivities in WP$_2$ single crystals. The WF holds at 2 K, but a downward deviation rapidly emerges upon warming. At 13 K, there is an exceptionally large mismatch between Lorenz number and the Sommerfeld value. We show that this is driven by a fivefold discrepancy between the $T$-square prefactors of electrical and thermal resistivities, both caused by electron-electron scattering. This implies the existence of abundant small-scattering-angle collisions between electrons, due to strong screening. By quantifying the relative frequency of collisions conserving momentum flux, but degrading heat flux, we identify a narrow temperature window where the hierarchy of scattering times may correspond to the hydrodynamic regime.