The thermal Hall conductivity of the trilayer cuprate ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$ (Hg1223)—the superconductor with the highest critical temperature $T_c$ at ambient pressure—was measured at temperatures down to 2 K for three dopings in the underdoped regime ($p=0.09,0.10,0.11$). By combining a previously introduced simple model and prior theoretical results, we derive a formula for the inverse mean free path, $1/\ell$, which allows us to estimate the mean free path of $d$-wave quasiparticles in Hg1223 below $T_c$. We find that $1/\ell$ grows as $T^3$, in agreement with the theoretical expectation for a clean $d$-wave superconductor. Measurements were also conducted on the single layer mercury-based cuprate ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{6+\delta }$ (Hg1201), revealing that the mean free path in this compound is roughly half that of its three-layered counterpart at the same doping $(p=0.10)$. This observation is attributed to the protective role of the outer planes in Hg1223, which results in a more pristine inner plane. We also report data in an ultraclean crystal of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO) with full oxygen content ($p=0.18$), believed to be the cleanest of any cuprate, and find that $\ell$ is not longer than in Hg1223.

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• Quasiparticles & collective excitations
• Thermal conductivity
• Transport phenomena
• Cuprates
• Unconventional superconductors
• Transport techniques