Single-particle spectral function of fractional quantum anomalous Hall states

Fractional quantum Hall states are the most prominent example of states with topological order, hosting excitations with fractionalized charge. Recent experiments in twisted <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mtext>MoTe</a:mtext><a:mn>2</a:mn></a:msub></a:math> 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. Charge fractionalization manifests itself in nearly momentum-independent spectra with a characteristic series of peaks determined from the filling fraction. The parton description qualitatively captures our numerical exact diagonalization results. Additionally, we discuss how the finite bandwidth of the Chern band and the nonideal 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 moiré lattices.