Exciton Gas versus Electron Hole Liquid in the Double Quantum Wells
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Exciton Gas versus Electron Hole Liquid in the Double Quantum Wells Vladimir S. Babichenko1 and Ilya Ya. Polishchuk1,2,3 1 RNC Kurchatov Institute, Kurchatov Sq.1, 123182, Moscow, Russia 2 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany 3 Moscow Institute of Physics and Technology, Institutskii per 9, Dolgoprudnii, Moscow Reg, 141700, Russia ABSTRACT The many-body correlation effects in the spatially separated electron and hole layers in the coupled quantum wells (CQW) are investigated. A special case of the many-component electron-hole system is considered, ߥ ͳ بbeing the number of the components. Keeping the main diagrams in the parameter ͳȀߥ allows us to justify the selection of the RPA diagrams. The ground state of the system is found to be the electron-hole liquid with the energy smaller than the dense exciton gas phase. The possible connection is discussed between the results obtained and the experiments in which the inhomogeneous state in the CQW is found. INTRODUCTION Investigation of spatially separated electrons and holes in double quantum wells was induced by the fact that such systems support the formation of bound electron-hole states (excitons) with a long lifetime [1] what makes possible observation of the Bose-Einstein condensation of the excitons. However, the phase diagram of such systems can be quite complicated (see, e.g., [2]). In this work we investigate how the Coulomb correlations influence the origin of the ground state of the system under consideration. The model of CQW assumes that electron move in one 2D layer and the holes move in the other 2D layer, these layers being separated by the distance l. At sufficiently low density and temperature, the electron-hole system may be considered as a degenerated exciton gas with interaction. However, with an increase in the exciton density n, when the distance between the particles n-1/2 becomes smaller or of the order of magnitude of the isolated exciton in-layer radius Rex, the system transforms into degenerated strongly correlated spatially separated electron-hole plasma. It is assumed that there exist ߥ ͳ بkinds of the electrons (holes). This approach was proposed in [3,4] to investigate the electron-hole plasma in many-valley semiconductors. Then, the diagrammatic expansion in ߥ ͳ بwas used to select the main diagrams. In this work, it is shown that the many-body Coulomb correlations result in the negative minimum in the ground state energy of the electron-hole system in the CQW. This minimum takes place at the certain density neq, and݊ ିଵȀଶ ൏ ܴ௫ . It occurs that this minimum is below the ground state energy of the exciton gas with the same density. It is shown that, if initial density n > neq, the system stays homogeneous; otherwise it decays into droplets of liquid phase. The possibility of the existence of the electron-hole droplets in conventional semiconductors was predicted in [5] and later confirmed in numerous theoretical and experimental works [6]. Finally, we discuss
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