Using coherent-state formalism (the Keldysh formalism), the article describes a transition from a homogeneous superfluid state to a supersolid state in a two-dimensional dilute gas of electron-hole pairs with spatially separated components. Such a transition is heralded by the appearance of a roton-type minimum in the collective excitation spectrum, which touches the abscissa axis as the distance between the layers or the pair density increases. This signals the instability of the system with respect to the appearance of a spatial modulation of the pair density. It has been found that a first-order transition to a hexagonal supersolid phase takes place a little earlier. A theory without phenomenological constants has been developed for an arbitrary relation between the effective masses of an electron and a hole. A phase diagram for the system has been plotted in the variables "the chemical potential of pairs - the distance between the layers". It has been shown that there is a jump in the average density of the condensate during the phase transition. It has been established that with an increase in the chemical potential, the inhomogeneous phase breaks up into high-density regions surrounded by lines at which the density becomes zero, with these lines forming a continuous network.

中文翻译：

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在电子-空穴对的二维稀气体中转变为超固相

使用相干态形式主义（Keldysh 形式主义），文章描述了在具有空间分离成分的电子-空穴对的二维稀释气体中从均质超流体状态到超固态的转变。这种转变是由集体激发光谱中旋转型最小值的出现预示的，随着层之间的距离或对密度的增加，它接触横坐标轴。这表示系统相对于对密度空间调制的出现的不稳定性。已经发现向六边形超固相的一级转变发生得稍早一些。已经为电子和空穴的有效质量之间的任意关系发展了一种没有现象学常数的理论。该系统的相图已绘制在变量“对的化学势 - 层之间的距离”中。已经表明，在相变期间冷凝物的平均密度存在跳跃。已经确定，随着化学势的增加，不均匀相分裂成被密度变为零的线包围的高密度区域，这些线形成连续的网络。