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Main Authors: Bollmann, Steffen, Haller, Andreas, Väyrynen, Jukka I., Schmidt, Thomas L., König, Elio J.
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2510.26686
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author Bollmann, Steffen
Haller, Andreas
Väyrynen, Jukka I.
Schmidt, Thomas L.
König, Elio J.
author_facet Bollmann, Steffen
Haller, Andreas
Väyrynen, Jukka I.
Schmidt, Thomas L.
König, Elio J.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_26686
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
Bollmann, Steffen
Haller, Andreas
Väyrynen, Jukka I.
Schmidt, Thomas L.
König, Elio J.
Strongly Correlated Electrons
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.
title Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
topic Strongly Correlated Electrons
url https://arxiv.org/abs/2510.26686