Electronic mean free path of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ from thermal Hall conductivity

TL;DR

This study measures the electronic mean free path in Bi2212 cuprate superconductors using thermal Hall conductivity, revealing shorter mean free paths compared to YBCO and highlighting the technique's effectiveness for comparing quasiparticle scattering.

Contribution

It introduces a method to estimate the electronic mean free path in cuprates via thermal Hall measurements, providing new insights into disorder levels across different doping regimes.

Findings

Mean free path in Bi2212 is about 7 times shorter than in YBCO.

Thermal Hall conductivity enhancement below T_c varies with doping and impurity scattering.

Underdoped samples show no enhancement, indicating higher disorder.

Abstract

We use thermal transport to access the electronic mean free path of $d$-wave quasiparticles in one of the most widely studied cuprate superconductors, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212). We have measured the thermal conductivity $\kappa_{\rm xx}$ and the thermal Hall conductivity $\kappa_{\rm xy}$ of three single crystals across a range of dopings. In the overdoped and optimally-doped samples, a clear enhancement is observed in both $\kappa_{\rm xx}$ and $\kappa_{\rm xy}$ upon cooling below the critical temperature $T_{\rm c}$, due to a suppression of the inelastic electron-electron scattering as electrons condense into pairs. The underdoped sample shows no enhancement in either, pointing to a high degree of disorder in that sample. For the two highest dopings, the magnitude of the enhancement in $\kappa_{\rm xy}$ is controlled by the strength of the elastic impurity scattering. Using a prior model to estimate the mean free path from $\kappa_{\rm xy}$ data, we find that the mean free path in Bi2212 is approximately 7 times shorter than in YBa$_2$Cu$_3$O$_7$, considered to be one of the least disordered cuprates. We conclude that the thermal Hall technique is a good way to compare the mean free path of $d$-wave quasiparticles in various cuprate materials.