Condensation of Excitons in Cu2O at Ultracold Temperatures: Experiment and Theory

We present experiments on the luminescence of excitons confined in a potential trap at milli-Kelvin bath temperatures under cw-excitation. They reveal several distinct features like a kink in the dependence of the total integrated luminescence intensity on excitation laser power and a bimodal distribution of the spatially resolved luminescence. Furthermore, we discuss the present state of the theoretical description of Bose-Einstein condensation of excitons with respect to signatures of a condensate in the luminescence. The comparison of the experimental data with theoretical results with respect to the spatially resolved as well as the integrated luminescence intensity shows the necessity of taking into account a Bose-Einstein condensed excitonic phase in order to understand the behaviour of the trapped excitons.Comment: 41 pages, 23 figure

Electron-Phonon Interaction in Tetrahedral Semiconductors

Effects of electron-phonon interactions on the band structure can be experimentally investigated in detail by measuring the temperature dependence of energy gaps or critical points (van Hove singularities) of the optical excitation spectra. These studies have been complemented in recent years by observing the dependence of such spectra on isotopic mass whenever different stable isotopes of a given atom are available at affordable prices. In crystals composed of different atoms, the effect of the vibration of each separate atom can thus be investigated by isotopic substitution. Because of the zero-point vibrations, such effects are present even at zero temperature (T = 0). In this paper we discuss state-of-the-art calculations of the dielectric function spectra and compare them with experimental results, with emphasis on the differences introduced by the electron-phonon interaction. The temperature dependence of various optical parameters will be described by means of one or two (in a few cases three) Einstein oscillators, except at the lowest temperatures where the T4 law (contrary to the Varshini T2 result) will be shown to apply. Increasing an isotopic mass increases the energy gaps, except in the case of monovalent Cu (e.g., CuCl) and possibly Ag (e.g., AgGaS2). It will be shown that the gaps of tetrahedral materials containing an element of the first row of the periodic table (C,N,O) are strongly affected by the electron-phonon interaction. It will be conjectured that this effect is related to the superconductivity recently observed in heavily boron-doped carbon.Comment: 17 pages, 17 fifure

Transition to a Bose-Einstein condensate of excitons at sub-Kelvin temperatures

Bose-Einstein condensation (BEC) is a quantum mechanical phenomenon directly linked to the quantum statistics of bosons. While cold atomic gases provide a new arena for exploring the nature of BEC, a long-term quest to confirm BEC of excitons, quasi-Bose particles formed as a bound state of an electron-hole pair, has been underway since its theoretical prediction in the 1960s. Ensembles of electrons and holes are complex quantum systems with strong Coulomb correlations; thus, it is non-trivial whether nature chooses a form of exciton BEC. Various systems have been examined in bulk and two-dimensional semiconductors and also exciton-photon hybrid systems. Among them, the 1s paraexciton state in a single crystal of Cu2O has been a prime candidate for realizing three-dimensional BEC. The large binding energy and long lifetime enable preparation of cold excitons in thermal equilibrium with the lattice and decoupled from the radiation field. However, collisional loss severely limits the conditions for reaching BEC. Such a system with a large inelastic cross section is excluded in atomic BEC experiments, where a small inelastic scattering rate and efficient elastic scattering are necessary for evaporative cooling. Here we demonstrate that it is nevertheless possible to achieve BEC by cooling paraexcitons to sub-Kelvin temperatures in a cold phonon bath. Emission spectra from paraexcitons in a three-dimensional trap show an anomalous distribution in a threshold-like manner at the critical number of BEC expected for ideal bosons. Bosonic stimulated scattering into the condensate and collisional loss compete and limit the condensate to a fraction of about 1%. This observation adds a new class of experimentally accessible BEC for exploring a rich variety of matter phases of electron-hole ensembles.Comment: 19 pages, 3 figures, Supplementary Information (12 pages, 4 figures) include