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Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moir\'e superlattice system $t$MoTe$_2$. 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, despite the absence of a magnetic field. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in $t$MoTe$_2$, at fillings $n=\frac{1}{2}$ and $n=\frac{3}{4}$. 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, which 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., Comment: 11 pages, including 3 sections of Supplemental Material and 6 figures

Moir\'e engineering in atomically thin van der Waals heterostructures creates artificial quantum materials with designer properties. We solve the many-body problem of interacting electrons confined to a moir\'e superlattice potential minimum (the moir\'e atom) using a 2D fermionic neural network. We show that strong Coulomb interactions in combination with the anisotropic moir\'e potential lead to striking ``Wigner molecule" charge density distributions observable with scanning tunneling microscopy.

Semiconductor moir\'e superlattices comprise an array of artificial atoms and provide a highly tunable platform for exploring novel electronic phases. We introduce a theoretical framework for studying moir\'e quantum matter that treats intra-moir\'e-atom interactions exactly and is controlled in the limit of large moir\'e period. We reveal an abundance of new physics arising from strong electron interactions when there are multiple electrons within a moir\'e unit cell. In particular, at filling factor $n=3$, the Coulomb interaction within each three-electron moir\'e atom leads to a three-lobed "Wigner molecule". When their size is comparable to the moir\'e period, the Wigner molecules form an emergent Kagome lattice. Our work identifies two universal length scales characterizing the kinetic and interaction energies in moir\'e materials and demonstrates a rich phase diagram due to their interplay., Comment: main 4 pages, 4 figures; supplement 11 pages, 3 figures. changes in v2: additional references and supplementary material added, minor changes to main text

The emergence of moir\'e materials with flat bands provides a platform to systematically investigate and precisely control correlated electronic phases. Here, we report local electronic compressibility measurements of a twisted WSe$_2$/MoSe$_2$ heterobilayer which reveal a rich phase diagram of interpenetrating Hofstadter states and electron solids. We show that this reflects the presence of both flat and dispersive moir\'e bands whose relative energies, and therefore occupations, are tuned by density and magnetic field. At low densities, competition between moir\'e bands leads to a transition from commensurate arrangements of singlets at doubly occupied sites to triplet configurations at high fields. Hofstadter states (i.e., Chern insulators) are generally favored at high densities as dispersive bands are populated, but are suppressed by an intervening region of reentrant charge-ordered states in which holes originating from multiple bands cooperatively crystallize. Our results reveal the key microscopic ingredients that favor distinct correlated ground states in semiconductor moir\'e systems, and they demonstrate an emergent lattice model system in which both interactions and band dispersion can be experimentally controlled.