Phases of Fractional Quantum (Anomalous) Hall -- Superconductor Quasi One-Dimensional Heterostructures
ORAL
Abstract
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 Z3 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, we established a phase diagram composed of Mott insulating phases, two different Luttinger liquids whose fundamental excitations carry charge 2e and 2e/3, respectively.
In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii–Kosterlitz–Thouless (BKT) as well as
a continuous Z3 x 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.
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 Z3 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, we established a phase diagram composed of Mott insulating phases, two different Luttinger liquids whose fundamental excitations carry charge 2e and 2e/3, respectively.
In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii–Kosterlitz–Thouless (BKT) as well as
a continuous Z3 x 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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Presenters
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Elio J König
- University of Wisconsin