Title: Correlated electronic states in MoSe₂ enabled by a periodic nanopatterned gate

Physical realizations of correlated electronic states have proven to be powerful tools in simulating quantum many-body interactions, altering electronic phase diagrams, and electronic band-engineering. Many of these systems have been enabled in recent years by transition metal dichalcogenides (TMDs), due in part to their enhanced Coulomb interactions and low-defect densities. Systems hosting correlated charge states are often realized by periodic moiré potentials that confine carriers to a superlattice. While these systems have proved fruitful, imprecise stacking techniques can lead to inconsistent moiré periodicities, and the states are geometrically constrained by the lattice structure of the moiré. I will present an alternative approach that enables customizable lattices to be engineered into monolayer MoSe₂. Using nano-scale gate patterning, we defined a 40 nm periodic, 2D triangular lattice of etched holes into a graphene gate that was integrated into an MoSe₂ heterostructure. Using gate-dependent, helicity-resolved differential reflectivity, we observe evidence of integer and fractional correlated states with enhanced magnetic interactions. We observed up to = 4 electron filling of the patterned lattice and enhanced Zeeman splitting that resulted in a maximum exciton g-factor of 20.