Stationary waves in a superfluid gas of electron-hole pairs in bilayers

Stationary waves in the condensate of electron-hole pairs in the n-p bilayer system are studied. The system demonstrates the transition from a uniform (superfluid) to a nonuniform (supersolid) state. The precursor of this transition is the appearance of the roton-type minimum in the collective mode spectrum. Stationary waves occur in the flow of the condensate past an obstacle. It is shown that the roton-type minimum manifests itself in a rather complicated stationary wave pattern, with several families of crests which cross one another. It is found that the stationary wave pattern is essentially modified under variation in the density of the condensate and under variation in the flow velocity. It is shown that the pattern is formed in the main part by short-wave modes in the case of a point obstacle. The contribution of long-wave modes is clearly visible in the case of a weak extended obstacle, where the stationary wave pattern resembles the ship wave pattern.