Anisotropic superfluidity of two-dimensional excitons in a periodic potential

We study anisotropies of helicity modulus, excitation spectrum, sound velocity and angle-resolved luminescence spectrum in a two-dimensional system of interacting excitons in a periodic potential. Analytical expressions for anisotropic corrections to the quantities characterizing superfluidity are obtained. We consider particularly the case of dipolar excitons in quantum wells. For GaAs/AlGaAs heterostructures as well as MoS$_2$/hBN/MoS$_2$ and MoSe$_2$/hBN/WSe$_2$ transition metal dichalcogenide bilayers estimates of the magnitude of the predicted effects are given. We also present a method to control superfluid motion and to determine the helicity modulus in generic dipolar systems.