Moir\'e Fractional Chern Insulators IV: Fluctuation-Driven Collapse of FCIs in Multi-Band Exact Diagonalization Calculations on Rhombohedral Graphene

TL;DR

This paper investigates the stability of fractional Chern insulators in rhombohedral graphene using unbiased multi-band exact diagonalization, revealing that band mixing and fluctuations tend to destroy FCI states previously predicted by simpler models.

Contribution

It demonstrates that multi-band fluctuations destabilize FCI states in rhombohedral graphene, challenging prior single-band projection results and highlighting the importance of considering full band mixing.

Findings

FCIs at ν=1/3 are destroyed by band mixing in multi-band calculations.

FCIs at ν=2/3 are initially strengthened but not stabilized in larger systems.

Single-band models may overestimate the stability of FCIs in this system.

Abstract

The fractional Chern insulators (FCIs) observed in pentalayer rhombohedral graphene/hexagonal boron nitride superlattices have a unique origin contrary to theoretical expectations: their non-interacting band structure is gapless, unlike standard FCIs and the Landau level. Hartree-Fock (HF) calculations at filling $\nu=1$ yield a gapped ground state with Chern number 1 through band mixing, identifying a possible parent state. However, many-body calculations restricted to the occupied HF band predispose the system towards FCIs and are essentially uncontrolled. In this work, we use unbiased multi-band exact diagonalization (ED) to allow fluctuations into the gapless bands for two normal-ordering schemes. In the "charge neutrality" scheme, the weak moir\'e potential leads to theoretical proposals based on Wigner crystal-like states. However, we find that FCIs seen in 1-band ED calculations are destroyed by band mixing, becoming gapless as fluctuations are included. In the "average" scheme, the Coulomb interaction with the periodic valence charge background sets up a stronger moir\'e potential. On small systems, FCIs at $\nu=1/3$ are destroyed in multi-band calculations, while those at $\nu=2/3$ are initially strengthened. However we do not converge to a stable FCI at $\nu=2/3$ even on the largest accessible systems. These findings question prior results obtained within projection to a single HF band. They suggest that current models do not support FCIs with correlation length small enough to be converged in accessible, unbiased ED calculations, or do not support FCIs at all.