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arXiv 2510.26686cond-mat.str-el
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准一维分数量子(反常)霍尔-超导体异质结构的相

Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures

Max-Planck Institute for Solid State Research(马克斯·普朗克固体研究所);University of Luxembourg(卢森堡大学);Purdue University(普渡大学);University of Wisconsin-Madison(威斯康星大学麦迪逊分校)

Steffen Bollmann, Andreas Haller, Jukka I. Väyrynen, Thomas L. Schmidt, Elio J. König

AI总结:

通过场论和密度矩阵重正化群模拟,研究存在U(1)序参量涨落的ν=2/3分数量子霍尔-超导体异质结构,揭示由Mott绝缘相和两种Luttinger液体组成的相图,并发现BKT型和连续Z3×U(1)二级相变。

摘要:

受最近在超导(SC)相附近观察到分数量子陈绝缘体(FCI)的启发,我们研究了存在$U(1)$序参量涨落的分数量子(反常)霍尔-超导体异质结构,并特别关注导致$\mathbb Z_3$ parafermions的$ν= 2/3$量子霍尔态。我们首先采用唯象场论定性确定相图。此外,我们推广了先前建立的超导和隧穿区域交替模式,该模式与分数量子霍尔边缘态耦合,将问题映射到涉及晶格parafermions的拓扑约瑟夫森结链。利用密度矩阵重正化群模拟,我们建立了一个由Mott绝缘相和两种Luttinger液体组成的相图,其基本激发分别携带电荷$2e$和$2e/3$。与使用共形场论的分析考虑一致,我们在数值上发现了Berezinskii-Kosterlitz-Thouless(BKT)型相变以及一个由中心荷c = 9/5表征的连续$\mathbb Z_3 \times U(1)$二级相变。我们最终提取了关于可能基态简并度的信息,并评论了在涨落存在下parafermionic边缘态的稳定性。这些理论基础预计对于moire材料中栅极定义的FCI-SC异质结构具有实际重要性,其中观察到了指示强序参量涨落的宽超导转变。

英文摘要:

Motivated by recent observations of fractional Chern insulators (FCIs) in the vicinity of superconducting (SC) phases, we study fractional quantum (anomalous) Hall-superconductor heterostructures in the presence of $U(1)$ order-parameter fluctuations and particularly focus on the case of $ν= 2/3$ quantum Hall states leading to $\mathbb Z_3$ parafermions. We first employ a phenomenological field theory to qualitatively determine the phase diagram. Furthermore, we generalize a previously established alternating pattern of superconductor and tunneling regions, coupled to fractional quantum Hall edge states, to map the problem onto a topological Josephson junction chain involving lattice parafermions. Using density matrix renormalization group simulations, we establish a phase diagram composed of Mott insulating phases and two different Luttinger liquids whose fundamental excitations carry charges 2e and $2e/3$, respectively. In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii-Kosterlitz-Thouless (BKT) type as well as a continuous $\mathbb Z_3 \times U(1)$ second-order phase transition characterized by central charge c = 9/5. We finally extract information about a possible ground state degeneracy and comment on the stability of parafermionic edge states in the presence of fluctuations. These theoretical foundations can be expected to be of practical importance for gate-defined FCI-SC heterostructures in moiré materials, in which broad superconducting transitions indicative of strong order parameter fluctuations were observed.

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