标题： 最强铜氧化物超导体中的热霍尔电导率：HgBa$_2$Ca$_2$Cu$_3$O$_{8 + $\delta$}$三层铜氧化物中自由程的估算 显示英文标题

标题： Thermal Hall conductivity in the strongest cuprate superconductor: Estimate of the mean free path in the trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8 + δ}$

摘要： 三重铜氧化物 HgBa$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ (Hg1223)——在环境压力下具有最高临界温度$T_c$的超导体——在三种欠掺杂情况（$p$ = 0.09, 0.10, 0.11）下的温度低至 2 K 时测量了其热霍尔电导率。 通过结合一个之前引入的简单模型和先前的理论结果，我们推导出逆平均自由程 $1 / \ell$ 的公式，这使我们能够估算在低于 $T_c$ 温度时 Hg1223 中 $d$ 波准粒子的平均自由程。 我们发现 $1 / \ell$ 随 $T^3$ 增长，与清洁条件下 $d$ 波超导体的理论预期一致。 同样还对单层汞基铜氧化物 HgBa$_2$CuO$_{6+\delta}$ (Hg1201) 进行了测量，结果显示在这种化合物中，自由程大约是其三层对应物的一半（掺杂水平相同，即$p$ = 0.10）。 这一观察结果可以归因于 Hg1223 中外层平面的保护作用，这使得内层平面更加“纯净”。 我们还报道了在超洁净的 YBa$_2$Cu$_3$O$_y$（YBCO）晶体中的数据，该晶体具有完全的氧含量$p$= 0.18，被认为是所有铜氧化物中最洁净的，并发现$\ell$并不比 Hg1223 更长。 显示英文摘要

摘要： The thermal Hall conductivity of the trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$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 HgBa$_2$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 can be 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 YBa$_2$Cu$_3$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.