标题： 无序超导的量子化输运：$ν=2/3$分数量子霍尔边缘态 显示英文标题

标题： Quantized Transport of Disordered Superconducting $ν=2/3$ Fractional Quantum Hall Edges

摘要： 分数量子霍尔（FQH）边缘态 $\nu=2/3$ 具有反向传播模式，已知在相关中性无序的作用下会流入一个稳定的Kane-Fisher-Polchinski（KFP）重正化群（RG）不动点，该不动点产生与实验一致的量子化的双端电导 $\frac{2}{3}\frac{e^2}{h}$。 受对超导（SC）量子霍尔系统日益增长的兴趣的推动，我们通过推广KFP分析研究了具有无序超导近邻效应的FQH边缘态 $\nu=2/3$，这也可以应用于最近实现的 $\nu=2/3$ 分数量子霍尔绝缘体。 我们证明了 $\nu=2/3$ 分数量子霍尔边缘态理论具有无限多个稳定的 RG 不动点 SC$_N$，它们由整数 $N\in\mathbb{Z}$标记，每个不动点均由相关的无序电荷-$2q_N$ SC 隧道驱动，且 $q_N\in\mathbb{Z}$的依赖关系取决于 $N$。 $N<0$（$N\ge0$）相由边缘处的吸引（排斥）模式间相互作用所支持。 我们进一步预测，在具有$q_N\neq0$的超导（SC）$_N$相中的边缘态会产生一个在 FQH-SC 结合点可以测量到的下游量化电阻$R_d=\frac{h}{2q_N^2e^2}$。 对于处于KFP相（$N=0$和$q_N=0$）下的边缘态，在SC近邻效应下，我们得到了非线性方程$R_d\propto V^{-\alpha}$或$T^{-\alpha}$，其中存在电压偏置$V$或温度$T$，而$\alpha=4$ （$\alpha=1$）取决于配对（涡旋隧穿）占主导地位。 显示英文摘要

摘要： The $\nu=2/3$ fractional quantum Hall (FQH) edge states, which have counter-propagating modes, are known to flow under relevant neutral disorders into a stable Kane-Fisher-Polchinski (KFP) renormalization group (RG) fixed point, which yields a quantized two-terminal conductance $\frac{2}{3}\frac{e^2}{h}$ consistent with the experiments. Motivated by growing interests in superconducting (SC) quantum Hall systems, we study the $\nu=2/3$ FQH edge states with disordered SC proximity by generalizing the KFP analysis, which may also apply to the recently realized $\nu=2/3$ fractional Chern insulator. We show that the $\nu=2/3$ FQH edge theory has an infinite number of stable RG fixed points SC$_N$ labeled by an integer $N\in\mathbb{Z}$, each of which is driven by a relevant disordered charge-$2q_N$ SC tunneling with $q_N\in\mathbb{Z}$ depending on $N$. The $N<0$ ($N\ge0$) phases are favored by an attractive (repulsive) inter-mode interaction on the edge. We further predict that the edge states in a SC$_N$ phase with $q_N\neq0$ yields a quantized downstream resistance $R_d=\frac{h}{2q_N^2e^2}$ measurable in a FQH-SC junction. For edge states staying in the KFP phase ($N=0$ and $q_N=0$) under SC proximity, we arrive at a nonlinear $R_d\propto V^{-\alpha}$ or $T^{-\alpha}$ with voltage bias $V$ or temperature $T$, where $\alpha=4$ ($\alpha=1$) if pairing (vortex tunneling) dominates.