Single-particle spectral function of fractional quantum anomalous Hall states

TL;DR

This paper develops a parton theory to analyze the single-particle spectral function of fractional quantum anomalous Hall states, providing insights into their fractionalized excitations and effects of band structure.

Contribution

It introduces a novel parton-based approach to characterize the spectral function of FQAH states, aligning with numerical results and considering realistic band effects.

Findings

Qualitative agreement between parton theory and exact diagonalization

Finite bandwidth and quantum geometry influence fractionalized excitations

Spectral function serves as a key tool for characterizing FQAH states

Abstract

Fractional quantum Hall states are the most prominent example of states with topological order, hosting excitations with fractionalized charge. Recent experiments in twisted $\text{MoTe}_2$ and graphene-based heterostructures provided evidence of fractional quantum anomalous Hall (FQAH) states, which spontaneously break time-reversal symmetry and persist even without an external magnetic field. Understanding the unique properties of these states requires the characterization of their low-energy excitations. To that end, we construct a parton theory for the energy and momentum-resolved single-particle spectral function of FQAH states. We explicitly consider several experimentally observed filling fractions as well as a composite Fermi liquid in the half-filled Chern band. The parton description qualitatively captures our numerical exact diagonalization results. Additionally, we discuss how the finite bandwidth of the Chern band and the non-ideal quantum geometry affect the fractionalized excitations. Our work demonstrates that the energy and momentum-resolved electronic single-particle spectral function provides a valuable tool to characterize fractionalized excitations of FQAH states in moir\'e lattices.