分数量子反常霍尔绝缘体-超导体异质结构中的Parafermions：自旋极化的作用
Parafermions in fractional Chern insulator-superconductor heterostructures: the role of spin polarization
AI总结：
本研究分析极化FQAH边缘沟道中的配对与隧穿通道，证明畴壁携带Z3 parafermions，并指出需要偶频等自旋配对，预期6π周期约瑟夫森电流。
AI中文摘要：
大多数关于分数量子霍尔-超导体结构中$Z_3$ parafermions的方案都使用了自旋非极化的$\nu = 2/3$ Halperin $(1,1,2)$态。扭曲MoTe$_2$和菱面体石墨烯的分数量子反常霍尔（FQAH）态被认为是自旋和谷极化的Jain态，具有相同的拓扑序但不同的自旋结构。我们分析了两个极化$\nu = 2/3$边缘之间的沟道。在边缘模式电子的配对和隧穿双线性项中，每种恰好有两个具有零共形自旋。配对仅与中性模式超导通道兼容，隧穿仅与中性模式背散射兼容，而在非极化态中，单重态配对和隧穿选择相同的通道。由于两个通道凝聚相同的中性任意子（相差一个局域算符），畴壁携带$Z_3$ parafermions，每对具有3个受保护态，无论中性通道在区域之间是否改变；固定费米子奇偶性不会增加此数量。在中性间隙形成之前，对于排斥性边缘间耦合，配对至多是边缘性的，除非吸引性中性耦合有利于其通道；一旦间隙形成，对于边缘间库仑耦合低于边缘内耦合的7/25，两个电荷项都是相关的。超导体必须提供偶频、等自旋、谷内配对，而具有仅Ising自旋轨道耦合的s波单重态超导体在领头阶不提供这种配对，而手性$p+ip$和$f+if$态则提供。$Z_3$标签由FQAH态的准粒子携带，因此任何局限于隧穿段不是FQAH的结的过程都不能改变它，我们预期在固定或不固定费米子奇偶性的情况下，约瑟夫森电流具有$6\pi$周期性。
英文摘要：
Most proposals for $Z_3$ parafermions in fractional quantum Hall-superconductor structures used the spin-unpolarized $ν= 2/3$ Halperin $(1,1,2)$ state. The fractional quantum anomalous Hall (FQAH) states of twisted MoTe$_2$ and rhombohedral graphene are believed to be spin- and valley-polarized Jain states, with the same topological order but a different spin structure. We analyze a trench between two polarized $ν= 2/3$ edges. Among the pairing and tunneling bilinears of the edge-mode electrons, exactly two of each have zero conformal spin. Pairing is compatible only with the neutral-mode superconductivity channel and tunneling only with neutral-mode backscattering, whereas in the unpolarized state singlet pairing and tunneling select the same channel. Since the two channels condense the same neutral anyon up to a local operator, the domain walls carry $Z_3$ parafermions, with 3 protected states per pair, whether or not the neutral channel changes between regions; fixing the fermion parity does not enlarge this count. Before the neutral gap forms, pairing is at best marginal for repulsive inter-edge coupling unless an attractive neutral coupling favors its channel; once the gap has formed, both charge terms are relevant for an inter-edge Coulomb coupling below 7/25 of the intra-edge one. The superconductor must supply even-frequency, equal-spin, intravalley pairing, which an s-wave singlet superconductor with only Ising spin-orbit coupling does not provide at leading order, whereas chiral $p+ip$ and $f+if$ states do. The $Z_3$ label is carried by a quasiparticle of the FQAH state, so no process confined to a junction whose tunneling segments are not FQAH can change it, and we expect a $6π$-periodic Josephson current with or without fixed fermion parity.
