We use thermal transport to access the electronic mean free path of $d$-wave quasiparticles in one of the most widely studied cuprate superconductors, ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (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 seven times shorter than in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$, 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.

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• Methods in superconductivity
• Superconductors
• Thermal techniques
• Transport techniques