Fractional Chern insulator candidate in twisted bilayer checkboard lattice

TL;DR

This paper demonstrates the potential realization of a fractional Chern insulator in twisted bilayer checkboard lattices with C=2, showing nearly ideal quantum geometry and characteristic many-body ground state degeneracy at fractional filling.

Contribution

It introduces a new candidate system for fractional Chern insulators in twisted bilayer checkboard lattices with C=2, supported by numerical evidence of topological order and quantum geometry.

Findings

Nearly flat bands with C=2 at magic angle

Nearly uniform Berry curvature and ideal quantum geometry

Ten-fold ground state degeneracy at 1/5 filling

Abstract

We investigate a fractional Chern insulator (FCI) candidate arising from Moir\'e bands with higher Chern number C=2 on a magic angle twisted bilayer checkboard lattice (MATBCB). There are two nearly flat low lying bands in the single particle energy spectrum under the first magic angle $\phi\approx 1.608^{\circ}$ and chiral limit. We find MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moir\'e Brillourin Zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a ten-fold ground state quasi-degeneracy in many body energy spectrum with filling fraction $\nu=1/5$. The ten-fold quasi-degenrate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasi-hole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a fractional Chern insulator is realized in this system.