Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice

TL;DR

This paper investigates the stability of the fractional Chern insulator phase during a transition from a checkerboard to a Lieb lattice, revealing conditions that enhance the many-body energy gap and support the FCI phase.

Contribution

It demonstrates how adding a sublattice influences the FCI phase stability and identifies parameter regions with larger energy gaps supporting the phase.

Findings

Interaction with additional sites can open or enlarge the energy gap.

Evidence of FCI phase found in parameter regions with larger gaps.

Topologically nontrivial flat bands support the FCI phase.

Abstract

The stability of $\nu=1/3$ Fractional Chern Insulator (FCI) phase is analysed on the example of checkerboard lattice undergoing a transition into Lieb lattice. The transition is performed by the addition of a second sublattice, whose coupling to the checkerboard sites is controlled by sublattice staggered potential. We investigate the influence of these sites on the many body energy gap between three lowest energy states and the fourth state. We consider cases with different complex phases acquired in hopping and a model with a flattened topologically nontrivial band. We find that an interaction with the additional sites either open the single-particle gap or enlarge the existing one, which translates into similar effect on the many-particle gap. Evidences of FCI phase for a region in a parameter space with larger energy gap are shown by looking at momenta of the three-fold degenerate ground state, spectral flow, and quasihole excitation spectrum.