Fractional Chern Insulators in Topological Flat bands with Higher Chern Number

TL;DR

This paper demonstrates the existence of new fractional Chern insulator states in flat bands with higher Chern numbers, revealing novel topological phases distinct from traditional quantum Hall states.

Contribution

It establishes the presence of stable fractional Chern insulator states in higher Chern number bands and characterizes their topological properties and differences from conventional quantum Hall states.

Findings

Stable fractional Chern insulator states at specific fillings

States are Abelian with unique topological degeneracies

Distinct from multilayer quantum Hall states due to band structure

Abstract

Lattice models forming bands with higher Chern number offer an intriguing possibility for new phases of matter with no analogue in continuum Landau levels. Here, we establish the existence of a number of new bulk insulating states at fractional filling in flat bands with Chern number $C=N>1$, forming in a recently proposed pyrochlore model with strong spin-orbit coupling. In particular, we find compelling evidence for a series of stable states at $\nu=1/(2N+1)$ for fermions as well as bosonic states at $\nu=1/(N+1)$. By examining the topological ground state degeneracies and the excitation structure as well as the entanglement spectrum, we conclude that these states are Abelian. We also explicitly demonstrate that these states are nevertheless qualitatively different from conventional quantum Hall (multilayer) states due to the novel properties of the underlying band structure.