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

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 ${\kappa }_{\mathrm{xx}}$ and the thermal Hall conductivity ${\kappa }_{\mathrm{xy}}$ of three single crystals across a range of dopings. In the overdoped and optimally-doped samples, a clear enhancement is observed in both ${\kappa }_{\mathrm{xx}}$ and ${\kappa }_{\mathrm{xy}}$ upon cooling below the critical temperature $T_{\mathrm{c}}$, 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 ${\kappa }_{\mathrm{xy}}$ is controlled by the strength of the elastic impurity scattering. Using a prior model to estimate the mean free path from ${\kappa }_{\mathrm{xy}}$ 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.