ISSN 0021-3640, JETP Letters, 2013, Vol. 97, No. 11, pp. 628–633. © Pleiades Publishing, Inc., 2013. Original Russian Text © V.S. Babichenko, I.Ya. Polishchuk, 2013, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2013, Vol. 97, No. 11, pp. 726–731. 628 Interest in studying double quantum wells has recently increased considerably owing to the opportu- nity of the experimental implementation of double quantum wells, in which electrons and holes are situ- ated in spatially separated regions with negligible tun- neling between the regions [1]. Investigation of spa- tially separated electrons and holes in double quantum wells was induced by the fact that such systems support the formation of electron–hole bound states (exci- tons) with a long lifetime [2]. This lifetime is several orders of magnitude longer than the lifetime of exci- tons in ordinary three-dimensional semiconductors, which facilitates the possibility of the observation of the Bose–Einstein condensation of excitons. Further investigation of such systems showed that their phase diagram can be quite complicated (see, e.g., [3]). In this work, we calculate the contribution of Cou- lomb correlations to the ground-state energy of a mul- ticomponent degenerate electron–hole plasma in a double quantum well. The model of a double quantum well studied below assumes that electrons and holes are spatially separated. The electrons move in a two- dimensional layer while the holes move in another one situated at the distance l from the first layer. Thus, we consider the case of the multicomponent spatially sep- arated electron–hole plasma. There are ν different sorts of electrons and the same number of sorts of holes and, in addition, ν  1. Thus, at a sufficiently low density of the system, the electrons and holes form bound states (excitons). At a sufficiently low tempera- ¶ In honor of Yu.M. Kagan’s anniversary. ture of the system, the plasma can be regarded as a degenerate Bose gas. However, with an increase in the density n of the electron–hole plasma, when the aver- age distance n –1/2 between the particles becomes smaller than or on the order of the radius R ex of an iso- lated exciton, the electron–hole bound state is destroyed and the system transforms into a degenerate strongly correlated plasma. The correlation energy of a multicomponent degenerate electron–hole plasma in ordinary three-dimensional multivalley semicon- ductors with the number of valleys ν  1 was first cal- culated in [4], where the selection of diagrams was based on the parameter 1/ν. This approach was further developed a decade later in [5]. In this work, it is shown that many-body Coulomb correlations lead to the existence of a negative mini- mum of the ground-state energy of the degenerate electron–hole plasma in a double quantum well as a function of the density n. More specifically, the mini- mum occurs at the density n eq , at which the average intralayer interparticle distance is smaller than the exciton size, < R ex . It turns out that this min- imum lies below the ground-state energy of the exci- ton gas, and, therefore, the energy ε eq of the system per particle is negative and, in addition, is greater that the exciton binding energy . Thus, it is energeti- cally unfavorable for the system to occur in the low- density state (n  n eq ) of an exciton gas. As a result, the system appears in the state of an electron–hole liquid. Furthermore, if the total number of particles is such n eq 1/2 – n eq 1/2 – ε eq ε ex Coulomb Correlations and Electron–Hole Liquid in Double Quantum Wells ¶ V. S. Babichenko a and I. Ya. Polishchuk a–c a National Research Centre Kurchatov Institute, pl. Akademika Kurchatova 1, Moscow, 123182 Russia e-mail: iyppolishchuk@gmail.com b Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany c Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow region, 141700 Russia Received April 23, 2013 It has been shown that many-body Coulomb correlations in double quantum wells with spatially separated electrons and holes result in the formation of a degenerate electron–hole liquid where an average distance between the particles is smaller than the size of an isolated exciton. This state turns out to be energetically more favorable than the exciton gas. The results have been obtained under the assumption that there are many different sorts of electrons and holes in the system, which is the case, in particular, in multivalley semicon- ductors. The relation to the experiments on the observation of luminescent regions in such systems is dis- cussed. DOI: 10.1134/S0021364013110027