Correlated phases of moat-band excitons in two-dimensional systems

We study two-dimensional systems of interacting excitons with a moat dispersion, for which the ground-state energy manifold presents a ring of discrete or continuously degenerate minima around a single point in momentum space. At low densities and for an idealized, perfectly degenerate moat, we show that the excitons undergo statistical transmutation and stabilize a chiral spin liquid. At higher densities, the moat dispersion favors Bose-Einstein condensation into states occupying multiple momenta, leading to inhomogeneous condensate phases and potentially supersolidity. We discuss the impact of band-structure warping present in realistic systems and argue that it generically stabilizes Bose-condensed phases over the chiral spin liquid, and analyze the superfluid response of the former which is unconventional due to the moat band. We also demonstrate that a proper renormalization of the exciton-exciton interaction is essential for describing these phases, and show that even purely repulsive interactions can favor inhomogeneous condensates. To further explore inhomogeneous condensate phases, we employ a Gross-Pitaevskii framework with a pseudopotential approximation and map out the resulting phase diagram. We show that the presence of degenerate dispersion minima can drive supersolidity already at weak coupling, in contrast to systems with a standard parabolic dispersion. Finally, we discuss our results in the context of real excitonic systems and argue that moat-band-induced supersolidity can be within experimental reach for realistic values of the model parameters.