Search

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 provide 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 captures qualitatively 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., Comment: 7+4 pages, 3+3 figures

Spin-ordered states close to metal-insulator transitions are poorly understood theoretically and challenging to probe in experiments. Here, we propose that the quantum twisting microscope, which provides direct access to the energy-momentum resolved spectrum of single-particle and collective excitations, can be used as a novel tool to distinguish between different types of magnetic order. To this end, we calculate the single-particle spectral function and the dynamical spin-structure factor for both a ferromagnetic and antiferromagnetic generalized Wigner crystal formed in fractionally filled moir\'e superlattices of transition metal dichalcogenide heterostructures. We demonstrate that magnetic order can be clearly identified in these response functions. Furthermore, we explore signatures of quantum phase transitions in the quantum twisting microscope response. We focus on the specific case of triangular moir\'e lattices at half filling, which have been proposed to host a topological phase transition between a chiral spin liquid and a 120 degree ordered state. Our work demonstrates the potential for quantum twisting microscopes to characterize quantum magnetism in moir\'e heterostructures., Comment: 9+11 pages, 3+2 figures