Fermionic non-Abelian fractional Chern insulators from dipolar interactions

TL;DR

This paper demonstrates the theoretical possibility of realizing non-Abelian fractional Chern insulators using dipolar interactions on a triangular lattice, providing a pathway for experimental topological quantum computing.

Contribution

It introduces a model with long-range dipolar interactions on a modified Hofstadter lattice to realize non-Abelian fractional Chern insulators, including Moore-Read and Read-Rezayi states.

Findings

Realization of non-Abelian $ u=1/2$ Moore-Read fractional Chern insulators.

Evidence for $ u=3/5$ Read-Rezayi fractional Chern insulators.

Potential for experimental implementation with realistic two-body interactions.

Abstract

We study fermions on a triangular lattice model that exhibits topological flatbands characterized by nonzero Chern numbers. Our scheme stems from the well-known Hofstadter model but the next-nearest-neighbor hopping is introduced, which is crucial for tuning the lowest band to be nearly flat. Differing from previous proposals with the necessity of multiparticle interactions, we consider the more realistic long-range dipolar interaction combined with two-body short-range attractions between fermions. We show the realization of the non-Abelian $\nu=1/2$ Moore-Read fractional Chern insulators, and strong evidence for the existence of the more exotic $\nu=3/5$ Read-Rezayi fractional Chern insulators. Our results provide insights for the experimental realization of these exotic states by realistic two-body interactions and thus facilitates the implementation of the universal topological quantum computation.