A transition into a supersolid phase in a two-dimensional diluted gas of electron-hole pairs
Within the approach based on the formalism of coherent states by L.V. Keldysh a transition from a homogeneous superfluid state to a supersolid state is described with reference to a diluted two-dimensional gas of electron-hole pairs with spatially separated components. A precursor of such a transition is the emergence the roton-type minimum in the spectrum of collective excitations, which, with increasing the distance between the layers or the density of the pairs touches to the abscissa axis, which signals instability of the system relative to the appearance of spatial modulation of the density of pairs. It is found that the first-order transition to the hexagonal supersolid phase takes place a little earlier. The theory is developed for an arbitrary ratio of effective masses of an electron and a hole and it does not contain phenomenological constants. The phase diagram of the system in coordinates «the chemical potential of the pairs - the distance between the layers» is built. It is shown that a phase transition is accompanied with a jump in the average density of the condensate. It is established that with an increase in the chemical potential, the inhomogeneous phase breaks up into high-density areas surrounded by lines on which the density is equal to zero, and these lines form a network.