Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene

TL;DR

This study explores how periodic circularly polarized light influences many-body phases in twisted bilayer graphene, revealing Floquet fractional Chern insulators and competing phases through numerical simulations.

Contribution

It introduces a high-frequency Floquet theory approach to identify and characterize Floquet fractional Chern insulators in twisted bilayer graphene.

Findings

Floquet fractional Chern insulators are found in a wide parameter range.

Topologically trivial charge density waves and Fermi liquids compete with fractional Chern insulators.

Effective static Hamiltonian captures key many-body phenomena under periodic driving.

Abstract

We study the many-body physics in twisted bilayer graphene coupled to periodic driving of a circularly polarized light when electron-electron interactions are taken into account. In the limit of high driving frequency $\Omega$, we use Floquet theory to formulate the system by an effective static Hamiltonian truncated to the order of $\Omega^{-2}$, which consists of a single-electron part and the screened Coulomb interaction. We numerically simulate this effective Hamiltonian by extensive exact diagonalization in the parameter space spanned by the twist angle and the driving strength. Remarkably, in a wide region of the parameter space, we identify Floquet fractional Chern insulator states in the partially filled Floquet valence bands. We characterize these topologically ordered states by ground-state degeneracy, spectral flow, and entanglement spectrum. In regions of the parameter space where fractional Chern insulator states are absent, we find topologically trivial charge density waves and band-dispersion-induced Fermi liquids which strongly compete with fractional Chern insulator states.