Thermal Hall conductivity in the strongest cuprate superconductor: Estimate of the mean free path in the trilayer cuprate HgBa₂Ca₂Cu₃O₈+δ

The thermal Hall conductivity of the trilayer cuprate HgBa₂Ca₂Cu₃O₈+_δ (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/ℓ, which allows us to estimate the mean free path of d-wave quasiparticles in Hg1223 below T_c. We find that 1/ℓ grows as T³, in agreement with the theoretical expectation for a clean d-wave superconductor. Measurements were also conducted on the single layer mercury-based cuprate HgBa₂CuO₆+_δ (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 YBa₂Cu₃O_y (YBCO) with full oxygen content (p = 0.18), believed to be the cleanest of any cuprate, and find that ℓ is not longer than in Hg1223.