Parafermions in Moir\'e Minibands

TL;DR

This paper explores the potential for realizing non-Abelian fractional Chern insulators with Fibonacci parafermion excitations in moiré minibands, supported by theoretical evidence from spectral analysis and entanglement spectra.

Contribution

It provides the first theoretical evidence for Fibonacci parafermion non-Abelian FCIs in moiré materials, expanding the understanding of exotic quantum phases.

Findings

Evidence from quantum numbers, spectral flow, and entanglement spectra supports non-Abelian FCIs.

Fibonacci parafermion excitations may be realized in moiré minibands.

Supports the potential for topologically protected quantum computation.

Abstract

Moir\'e materials provide a remarkably tunable platform for topological and strongly correlated quantum phases of matter. Very recently, the first zero field Abelian fractional Chern insulators (FCIs) have been experimentally demonstrated and it has been theoretically predicted that non-Abelian states with Majorana fermion excitations may be realized in the nearly dispersionless minibands of these systems. Here we provide telltale evidence in terms of low-energy quantum numbers, spectral flow and entanglement spectra for the even more exotic possibility of moir\'e-based non-Abelian FCIs exhibiting Fibonacci parafermion excitations.