Two-dimensional dipolar bosons with weak disorder

We consider two-dimensional dipolar bosonic gas with dipoles oriented perpendicularly to the plane in a weak random potential. We investigate analytically and numerically the condensate depletion, the one-body density-matrix, the ground state energy, the sound velocity and the superfluid fraction. Concentrating on the regime where a roton-like excitation spectrum forms, our results show that the superfluidity disappears below a critical value of disorder strength yielding the transition to a non-trivial quantum regime.