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Non-Abelian topological superconductivity from melting Abelian fractional Chern insulators

Zhengyan Darius Shi, T. Senthil

TL;DR

The paper develops a unified field-theoretic framework to connect a Jain fractional Chern insulator at ν=2/3 with multiple neighboring superconducting phases by tuning bandwidth. It leverages three equivalent U(2) and U(1) Chern-Simons descriptions of Jain_2/3 to identify five continuous transitions to superconductors, including non-Abelian topological superconductors with Majorana modes, some realized when the electron gap remains open and others when it closes. The key results include bosonic and fermionic quantum critical points described by Nf=3 QED-CS or Nf=3 QCD-CS theories, and additional pathways involving bosonic partons that yield charge-4e SC* states with SU(2)_{±4}/Z2 topological order. The findings provide a concrete EFT roadmap for Jain-state to superconductor transitions, yielding predictions testable by numerics (e.g., chiral central charges, gap closures) and guiding future studies of exotic superconductivity in lattice systems.

Abstract

Fractional Chern insulators (FCI) are exotic phases of matter realized at partial filling of a Chern band that host fractionally charged anyon excitations. Recent numerical studies in several microscopic models reveal that increasing the bandwidth in an FCI can drive a direct transition into a charge-2e superconductor rather than a conventional Fermi liquid. Motivated by this surprising observation, we propose a theoretical framework that captures the intertwinement between superconductivity and fractionalization in a lattice setting. Leveraging the duality between three field-theoretic descriptions of the Jain topological order, we find that bandwidth tuning can drive a single parent FCI at $ν= 2/3$ into five different superconductors, some of which are intrinsically non-Abelian and support Majorana zero modes. Our results reveal a rich landscape of exotic superconductors with no normal state Fermi surface and predict novel higher-charge superconductors coexisting with neutral non-Abelian topological order at more general filling fractions $ν= p/(2p+1)$.

Non-Abelian topological superconductivity from melting Abelian fractional Chern insulators

TL;DR

The paper develops a unified field-theoretic framework to connect a Jain fractional Chern insulator at ν=2/3 with multiple neighboring superconducting phases by tuning bandwidth. It leverages three equivalent U(2) and U(1) Chern-Simons descriptions of Jain_2/3 to identify five continuous transitions to superconductors, including non-Abelian topological superconductors with Majorana modes, some realized when the electron gap remains open and others when it closes. The key results include bosonic and fermionic quantum critical points described by Nf=3 QED-CS or Nf=3 QCD-CS theories, and additional pathways involving bosonic partons that yield charge-4e SC* states with SU(2)_{±4}/Z2 topological order. The findings provide a concrete EFT roadmap for Jain-state to superconductor transitions, yielding predictions testable by numerics (e.g., chiral central charges, gap closures) and guiding future studies of exotic superconductivity in lattice systems.

Abstract

Fractional Chern insulators (FCI) are exotic phases of matter realized at partial filling of a Chern band that host fractionally charged anyon excitations. Recent numerical studies in several microscopic models reveal that increasing the bandwidth in an FCI can drive a direct transition into a charge-2e superconductor rather than a conventional Fermi liquid. Motivated by this surprising observation, we propose a theoretical framework that captures the intertwinement between superconductivity and fractionalization in a lattice setting. Leveraging the duality between three field-theoretic descriptions of the Jain topological order, we find that bandwidth tuning can drive a single parent FCI at into five different superconductors, some of which are intrinsically non-Abelian and support Majorana zero modes. Our results reveal a rich landscape of exotic superconductors with no normal state Fermi surface and predict novel higher-charge superconductors coexisting with neutral non-Abelian topological order at more general filling fractions .

Paper Structure

This paper contains 12 sections, 42 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Three descriptions of the Jain FCI at
  3. Superconductivity from melting the Jain FCI at
  4. Bosonic QCP: gap closing of
  5. Fermionic QCP: gap closing of
  6. Discussion
  7. gauge theory for fermionic Jain states
  8. A family of superconductors described by gauge theories
  9. Bandwidth-tuned Jain-SC transition at general filling
  10. Superconductivity from the Abelian representation of
  11. Superconductivity from non-Abelian representations of
  12. -symmetric transition between a boson IQH state and a boson Mott insulator

Figures (2)

  • Figure 1: Five distinct superconductors that can be accessed from the Jain state at $\nu = 2/3$ through a direct bandwidth-tuned quantum phase transition. Note that closing/not closing the electron gap leads to superconductors with half-integer/integer chiral central charge $c_-$.
  • Figure 2: For $p \neq 1, -2$, we find four higher-charge superconductors accessible from the Jain FCI at $\nu = p/(2p+1)$ through a bandwidth-tuned phase transition. $\Delta_q$ is the energy gap of the anyon with fractional charge $q$ and the two families of transitions involve gap closing of $\Delta_{\nu}$ and $\Delta_{1-\nu}$ respectively.