Superfluidity of a dilute gas of electron-hole pairs in a bilayer system

Abstract

The conditions of stability of the superfluid phase in double layer systems with pairing of spatially separated electrons and holes in the low density limit are studied. The general expression for the collective excitation spectrum is obtained. It is shown that under increase in the distance d between the layers the minimum emerges in the excitation spectrum. When d reaches the critical value the superfluid state becomes unstable relative to the formation of a kind of the Wigner crystal state. The same instability occurs at fixed d under increase in the density of carries. It is established that the critical distance and the critical density are related to each other by the inverse power function. The impact of the impurities on the temperature of the superfluid transition is investigated. The impact is found weak at the impurity concentration smaller than the density of the pairs. It is shown that in the rarefied system the critical temperature Tc ≈ 100 K can be reached.

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

“…III and IV. In [24], we found the collective mode spectrum for the exciton BEC at rest. Here we obtain the collective mode spectrum in the flowing condensate.…”

“…In this section, we review the coherent wave-function approach to the description of BEC of spatially indirect excitons [22,24] and derive formulas used for the calculation of the stationary wave patterns in Secs. III and IV.…”

“…In the high-density limit, these excitons are similar to Cooper pairs in superconductors, and the description of such systems can be given in the framework of a modified version [16][17][18][19][20] of the Bardin-Cooper-Schrieffer (BCS) theory [21]. In the low-density limit the approach based on the Keldysh wave function [22] can be used [23,24]. The superfluidity of spatially indirect excitons can be considered as a special kind of superconductivity [16,17].…”

“…The approach was proposed by Keldysh [22] for a description of the coherent state of excitons in three-dimensional systems (without spatial separation of carriers). In [24,56], the approach [22] was used for the analysis of the conditions of stability of the BEC of electron-hole pairs in bilayers and the transition of such a BEC to the supersolid state. The spectrum obtained in [24] (much like the collective excitation spectrum in quantum Hall bilayers [26]) has a roton-type minimum close to the superfluid-supersolid transition line [56][57][58].…”

“…In [24,56], the approach [22] was used for the analysis of the conditions of stability of the BEC of electron-hole pairs in bilayers and the transition of such a BEC to the supersolid state. The spectrum obtained in [24] (much like the collective excitation spectrum in quantum Hall bilayers [26]) has a roton-type minimum close to the superfluid-supersolid transition line [56][57][58]. This transition is similar to the superfluid-supersolid transition in dipole Bose gases [59][60][61][62][63].…”