Signatures of the superfluid-Mott Transition in van der Waals Excitonic Lattices

We develop a Bose–Hubbard framework for spin-triplet excitons in two-dimensional van der Waals heterostructures realizing engineered lattices—from conventional moiré minibands to deliberately patterned Kagome geometries with flat and Dirac bands. Spin-triplet excitons occupy lattice sites with hopping , a spin-independent on-site interaction (density–density), a spin-dependent on-site exchange (spin–spin), and a weak nearest-neighbor repulsion . At commensurate filling and large , the ground state is a Mott insulator with a charge gap and suppressed number fluctuations. We show that lowering the exciton density (or, equivalently, increasing via gate-controlled lattice depth/screening) drives a superfluid-Mott transition. In Kagome lattices, geometric frustration and the flat band enhance interaction effects: we predict density-tuned realization of flat-band superfluidity, possible chiral superfluid phases under weak time-reversal-symmetry breaking and enlarged Mott lobes near van Hove fillings. We provide clear theoretical signatures of the superfluid-Mott transition, which could be verified in future experiments. Our results establish moiré/Kagome excitonic lattices as a platform for spinful bosonic Hubbard physics and programmable quantum fluidics with nontrivial band topology.