Exciton condensate in semiconductor quantum well structures.

We propose that the exciton condensate may form in a well-controlled way in appropriately arranged semiconductor quantum well structures. The mean-field theory of Keldysh and Kopaev, exact in both the high density and the low density limits, is solved numerically to illustrate our proposal. The electron-hole pairing gap and the excitation spectrum of the exciton condensate are obtained. The energy scales of the condensate are substantial at higher densities. We discuss how such densities could be achieved experimentally by generating an effective pressure. PACS numbers: 71.35.+z,73.20.Dz Typeset using REVTEX 1 The issue of Bose-Einstein condensation of excitons has been extensively studied, following the early suggestion by Keldysh and Kopaev [1–3]. In the intervening years, it continues to be a subject of considerable experimental and theoretical interest [4–10]. Until recently, much of the experimental work has been carried out on indirect semiconductors [1]. In view of the great advances made in our abilities to design and manufacture high quality artificial semiconductor quantum well (QW) structures, it appears opportune to investigate in some detail the possible exciton condensate states in direct gap semiconductors. The crux of the matter lies in obtaining an exciton fluid at sufficiently high densities and low temperatures to realize a condensed phase. Recent experiments on Cu2O [10] and on GaAs quantum wells in high magnetic fields [9] appear quite promising. However, detailed and unambiguous interpretation of these experiments has been difficult either because of the low density obtained in QWs (where it has been argued that disorder dominates the photoluminescence spectrum [8]) or because of non-equilibrium and/or time-dependence of the density [10]. Clearly it would be very desirable to be able to produce exciton fluids at controlled, and possibly higher, densities. This has two advantages: the energy scale of the condensate would be larger and the variation of key properties with density could be systematically examined. Other fundamental questions related to the dynamics of condensation, possible lasing action, superradiance and coupling to a coherent photon field could be studied experimentally under controlled conditions. Our proposal is to tailor the QW parameters in double well electron-hole systems so as to generate an effective pressure on part of the exciton fluid and thereby achieve the physical conditions necessary for a controlled formation of exciton condensates. To this end, we set up and numerically solve the mean-field theory (MFT) proposed earlier by Keldysh and Kopaev [2,5,6], exact in both the high and low density limits, to obtain the total energy as a function of arbitrary densities for a variety of interlayer separation of the double layer QWs. The same MFT is also used to study the excitation properties of the proposed exciton droplet, which are crucial to its stability against small perturbations such as finite temperature, interface disorder, and complications arising from the band structure 2 of the underlying semiconductors. At T = 0 the exciton fluid for the idealized system is an insulating Bose-Einstein condensate at all densities, i.e., there exists a gap to all charged excitations. Hence it has been called an excitonic insulator. We begin by examining the ideal two-dimensional (2D) electron-hole system, characterized by the following Hamiltonian: