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Topological Charge-2ne Superconductors

Zhi-Qiang Gao, Yan-Qi Wang, Hui Yang, Congjun Wu

TL;DR

By developing a unified wavefunction and bulk-edge TQFT framework, the paper constructs topological charge-2ne superconductors from charge-2e ingredients and via breaking U(1) symmetry in fractional quantum Hall states. The Read-Green-based construction uses an edge CFT and spin TQFT to realize charge-2ne condensates, with a U(2n) bulk CS description; for n=1 it recovers the (p+ip) superconductor, and for higher n it reveals nonabelian vortex content. The alternative parafermion approach absorbs Laughlin factors to produce consistent, fermionic nonabelian spin TQFTs described by CS theories such as S[U(2)^{⊗n}]_{2n,0} and related constructions, including detailed spectra for specific n. Overall, the work provides a coherent low-energy description of topological charge-2ne superconductivity and outlines concrete experimental probes, such as interferometry and Josephson effects, to detect these exotic phases.

Abstract

Charge-$4e$ superconductors are phases where quartets of electrons condense in the absence of Cooper pairing condensation. They exhibit distinctive signatures including fractional flux quantization and anomalous Josephson effects, and are actively being explored in strongly correlated systems, such as moiré materials. In this work we develop a general framework for \emph{topological} charge-$2ne$ superconductors based on both wavefunction and field theory approaches. In particular, we generate topological charge-$2ne$ superconductors from charge-$2e$ ingredients, and by breaking the charge $U(1)$ symmetry in certain classes of quantum Hall states. Via bulk-edge correspondence, we further construct the corresponding edge conformal field theory and bulk topological quantum field theory for topological charge-$2ne$ superconductors that suggests fermionic nonabelian topological orders. Our results provide a unified low energy description of the topological charge-$2ne$ superconductivity, offer a concrete platform for studying symmetry breaking and enrichment in interacting topological phases of matter, and have direct implications for experimental probes such as quasiparticle interferometry.

Topological Charge-2ne Superconductors

TL;DR

By developing a unified wavefunction and bulk-edge TQFT framework, the paper constructs topological charge-2ne superconductors from charge-2e ingredients and via breaking U(1) symmetry in fractional quantum Hall states. The Read-Green-based construction uses an edge CFT and spin TQFT to realize charge-2ne condensates, with a U(2n) bulk CS description; for n=1 it recovers the (p+ip) superconductor, and for higher n it reveals nonabelian vortex content. The alternative parafermion approach absorbs Laughlin factors to produce consistent, fermionic nonabelian spin TQFTs described by CS theories such as S[U(2)^{⊗n}]_{2n,0} and related constructions, including detailed spectra for specific n. Overall, the work provides a coherent low-energy description of topological charge-2ne superconductivity and outlines concrete experimental probes, such as interferometry and Josephson effects, to detect these exotic phases.

Abstract

Charge- superconductors are phases where quartets of electrons condense in the absence of Cooper pairing condensation. They exhibit distinctive signatures including fractional flux quantization and anomalous Josephson effects, and are actively being explored in strongly correlated systems, such as moiré materials. In this work we develop a general framework for \emph{topological} charge- superconductors based on both wavefunction and field theory approaches. In particular, we generate topological charge- superconductors from charge- ingredients, and by breaking the charge symmetry in certain classes of quantum Hall states. Via bulk-edge correspondence, we further construct the corresponding edge conformal field theory and bulk topological quantum field theory for topological charge- superconductors that suggests fermionic nonabelian topological orders. Our results provide a unified low energy description of the topological charge- superconductivity, offer a concrete platform for studying symmetry breaking and enrichment in interacting topological phases of matter, and have direct implications for experimental probes such as quasiparticle interferometry.
Paper Structure (14 sections, 29 equations, 1 figure, 2 tables)

This paper contains 14 sections, 29 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Topological Charge-$2ne$ superconductivity from the Read-Green Wavefunction
  3. Topological Charge-$2ne$ superconductivity from Breaking Charge Conservation
  4. Failure of Breaking Charge Conservation in Read-Rezayi State
  5. Construction through Composite $\mathbb{Z}_{2n}$ Parafermion
  6. Spectrum of Topological Charge-$2ne$ Superconductors
  7. Discussion
  8. Acknowledgment
  9. Anyon content of the $U(4)_{4,0}$ TQFT
  10. Derivation of bulk TQFTs
  11. Derivation of $\mathcal{S}[U(2n)^{\otimes p}]_{k,0}$ TQFT
  12. Relation between $2n$-cluster and Moore-Read states
  13. Derivation of $\mathcal{S}[U(2)^{\otimes 2n}]_{2n,0}$ TQFT
  14. Anyon content of $\mathcal{S}[U(2)\times U(2)]_{4,0}$ TQFT

Figures (1)

  • Figure 1: Illustration of generalizing the Read-Green wavefunction (left pannel) and breaking charge $U(1)$ symmetry from the Read-Rezayi state (right pannel), using charge-$4e$ as an example. The blue dots represent electrons. Each gray thin line segment represents a $\tilde{g}(z-z^\prime)$ factor ($(p+ip)$-wave pairing).