Field-tuned and zero-field fractional Chern insulators in magic angle graphene

TL;DR

This paper provides a detailed theoretical analysis of fractional Chern insulators in magic angle graphene, highlighting how magnetic fields stabilize these states by reducing bandwidth and improving quantum geometry, with implications for zero-field realizations.

Contribution

The authors introduce generalized quantum geometry for Hofstadter minibands and extend Hartree-Fock theory to finite fields, advancing understanding of FCI stabilization in magic angle graphene.

Findings

Magnetic field reduces effective bandwidth and enhances quantum geometry for FCIs.

DMRG simulations identify parameter regimes where FCIs are stable.

Zero-field charge density wave states transition to FCIs at specific magnetic fluxes.

Abstract

In contrast to the fractional quantum Hall (FQH) effect, where electron density fixes the applied magnetic field, fractional Chern insulators (FCIs) can realize FQH states in comparatively weak or even zero magnetic fields. Previous theoretical work highlighted magic angle graphene as a promising FCI platform, satisfying the twin requirements of flat bands and lowest-Landau-level-like quantum geometry. Indeed, recent experiments have demonstrated FCIs in magic angle graphene with weak magnetic fields. Here we conduct a detailed theoretical study of the most prominent FCI state observed, and clarify the role of the magnetic field in stabilizing this state. We introduce two new technical tools: first, we generalize the notion of ideal quantum geometry to Hofstadter minibands and, second, we extend the Hartree-Fock theory of magic-angle graphene to finite field, to account for the interaction generated bandwidth. We show that magnetic field both dramatically reduces the effective bandwidth and improves the quantum geometry for hosting FCIs. Using density matrix renormalization group (DMRG) simulations of a microscopic model of magic angle graphene, we establish the regime of bandwidth and quantum geometry indicators where FCIs are stabilized. Further characterizing the finite-field bands by the same quantities we show how a zero-field charge density wave state gives way to an FCI state at a magnetic flux consistent with experiment. We also speculate on the other FCIs seen in the same experiments, including anomalous incompressible states and even-denominator fractions which may host non-Abelian states. Finally, when bandwidth is the limiting factor, we propose a range of experimental parameters where FCIs should appear at zero magnetic field.