Zero-Field Composite Fermi Liquid in Twisted Semiconductor Bilayers.

Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moiré superlattice system tMoTe_{2}. Here, we argue that a composite fermion description, already a unifying framework for the phenomenology of 2D electron gases at high magnetic fields, provides a similarly powerful perspective in this new context. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in tMoTe_{2} at fillings n=1/2 and n=3/4. We dub these non-Fermi liquid metals anomalous composite Fermi liquids (ACFLs), and we argue that they play a central organizing role in the FQAH phase diagram. We proceed to develop a long wavelength theory for this ACFL state that offers concrete experimental predictions upon doping the composite Fermi sea, including a Jain sequence of FQAH states and a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system.

Superconductivity and strong interactions in a tunable moiré quasicrystal.

Electronic states in quasicrystals generally preclude a Bloch description1, rendering them fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are underexplored relative to periodic and amorphous structures. Here we introduce a new type of highly tunable quasicrystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two mutually incommensurate moiré patterns. In contrast to many common atomic-scale quasicrystals2,3, the quasiperiodicity in our system is defined on moiré length scales of several nanometres. This 'moiré quasicrystal' allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Notably, in the quasiperiodic regime, we observe superconductivity near a flavour-symmetry-breaking phase transition4,5, the latter indicative of the important role that electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems but may also provide insights into electronic ordering in related periodic moiré crystals6-12. We anticipate that extending this platform to engineer quasicrystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasicrystals.

Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures.

van der Waals (vdW) heterostructures formed by two-dimensional (2D) magnets and semiconductors have provided a fertile ground for fundamental science and spintronics. We present first-principles calculations finding a proximity exchange splitting of 14 meV (equivalent to an effective Zeeman field of 120 T) in the vdW magnet-semiconductor heterostructure MoS 2/CrBr 3, leading to a 2D spin-polarized half-metal with carrier densities ranging up to 1013 cm-2. We consequently explore the effect of large exchange coupling on the electronic band structure when the magnetic layer hosts chiral spin textures such as skyrmions. A flat Chern band is found at a "magic" value of magnetization [Formula: see text] for Schrödinger electrons, and it generally occurs for Dirac electrons. The magnetic proximity-induced anomalous Hall effect enables transport-based detection of chiral spin textures, and flat Chern bands provide an avenue for engineering various strongly correlated states.

Moiré Landau Fans and Magic Zeros.

We study the energy spectrum of moiré systems under a uniform magnetic field. The superlattice potential generally broadens Landau levels into Chern bands with finite bandwidth. However, we find that these Chern bands become flat at a discrete set of magnetic fields which we dub "magic zeros." The flat band subspace is generally different from the Landau level subspace in the absence of the moiré superlattice. By developing a semiclassical quantization method and taking account of superlattice induced Bragg reflection, we prove that magic zeros arise from the simultaneous quantization of two distinct k-space orbits. For instance, we show the chiral model of TBG has flat bands at special fields for any twist angle in the nth Landau level for |n|>1. The flat bands at magic zeros provide a new setting for exploring crystalline fractional quantum Hall physics.