Phases of itinerant anyons in Laughlin's quantum Hall states on a lattice

TL;DR

This paper investigates the phases of itinerant anyons in Laughlin-like fractional Chern insulators, revealing how band topology and symmetry influence the emergence of anyon superconductivity, especially near the $ u=1/3$ state.

Contribution

It introduces a theoretical and numerical analysis of doped fractional Chern insulators, highlighting the role of symmetry and Berry curvature in realizing different anyonic phases and uncovering a new mechanism for anyon superconductivity.

Findings

Dependence of anyonic phases on U(1) or SU(m) Chern-Simons descriptions.

Interplay between Berry curvature and anyon dispersion affects phase realization.

Identification of a mechanism for anyon superconductivity with half-integer central charge.

Abstract

We study phases of itinerant anyons when hole-doping Laughlin-like states in fractional Chern insulators (FCIs). In light of the recent observation of time-reversal-broken superconductivity near FCIs in van der Waals materials, a theoretical understanding of doped fractional quantum Hall states on a lattice has been developed by Shi and Senthil [Phys. Rev. X 15, 031069], reviving old ideas about "anyon superconductivity". We test these ideas analytically within an effective parton mean-field theory and numerically with variational Monte Carlo, pointing out that the predicted state depends on whether the Laughlin order at $\nu=1/m$ is described by a U(1), or an SU(m) Chern-Simons field, the latter implying a symmetry between the m parton species. Our results demonstrate that the interplay between band Berry curvature and effective anyon dispersion has crucial implications for which anyonic phase is realized. In the experimentally relevant scenario of hole-doping the $\nu=1/3$ fermionic FCI, our results uncover a mechanism for the formation of an anyon superconducting state of half-integer central charge in the case when the energetically cheapest excitations are the fundamental 1/3 charge anyons, bypassing the need for these anyons to pair into charge-2/3 composites, which has generally been assumed in similar anyon superconductivity constructions.