We present experiments on the luminescence of excitons confined in a potential trap at sub-Kelvin temperatures after nanosecond pulsed laser excitation. Analysis of the experimental results with a rate model shows that the so-called Auger decay of yellow excitons, which in previous studies led to a rapid decay of the excitons at high densities and thus prevented reaching the critical density for Bose-Einstein condensation (BEC), is greatly reduced for paraexcitons. We demonstrate that exciton numbers well above 10 10 can be collected in a potential trap, albeit at temperatures in the 10 K range. During their lifetime of about 500 ns the paraexcitons cool down to the temperature of the He bath. This opens up the possibility to observe a BEC of paraexcitons provided that the bath temperature can be reduced to below 100 mK.(1) with 0 being the average oscillator frequency of the trapping potential and ζ the Riemann zeta function, decreases much faster with temperature, T , than in free space.Due to their unique properties, the excitons of the so-called yellow series in the semiconductor cuprous oxide (Cu 2 O) are still considered one of several promising candidates for excitonic BEC (for reviews see [4][5][6]). This is related to the large binding energy of 150 meV, which shifts the Mott density to 10 19 cm −3 at cryogenic temperatures [7,8]. Made up of doubly degenerate valence and conduction bands, the ground state of this series splits into the triply degenerate orthoexciton and the nondegenerate paraexciton, which is the energetically lowest exciton state, = 12.1 meV below the orthoexciton states. Due to the positive parity of the bands, the orthoexciton is only weakly optically allowed (quadrupole transition with oscillator
We present experiments on the luminescence of excitons confined in a potential trap at milli-Kelvin bath temperatures under continuous-wave (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.
We show that in a magnetic field B the otherwise forbidden lowest exciton in Cu2O (paraexciton of Gamma(2)(+) symmetry) gives rise to a narrow absorption line of 80 neV at a temperature of 1.2 K. The B2 dependence of the field-induced oscillator strength and the low energy shift DeltaE with increasing field strength are measured. From two-phonon excitation spectroscopy measurements we derive by a merely kinematical analysis a very reliable value for the paraexciton mass. A blueshift and a broadening of the absorption line are observed for increasing excitation intensity. These observations are discussed in connection with a Bose-Einstein condensation of paraexcitons in Cu2O.
The basic theoretical foundation for the modelling of phonon-assisted absorption spectra in direct bandgap semiconductors, introduced by Elliott 60 years ago 1 using second order perturbation theory, results in a square root shaped dependency close to the absorption edge. A careful analysis of the experiments 2 reveals that for the yellow S excitons in Cu2O the lineshape does not follow that square root dependence. The reexamination of the theory shows that the basic assumptions of constant matrix elements and constant energy denominators is invalid for semiconductors with dominant exciton effects like Cu2O, where the phonon-assisted absorption proceeds via intermediate exciton states. The overlap between these and the final exciton states strongly determines the dependence of the absorption on the photon energy. To describe the experimental observed line shape of the indirect absorption of the yellow S exciton states we find it necessary to assume a momentum dependent deformation potential for the optical phonons.
We have found a series of resonances associated with the bound state (polyexcitons, PE(N)s) of N excitons up to N=6 in the emission spectra of diamond under two-photon excitation at around 10 K. Time-resolved spectra show a stepwise formation of PE(N)s with smaller to larger N, as well as a successive decay from larger to smaller N. At higher excitation levels, the transformation of PE(N)s into a condensed phase of electron-hole droplets occurs. The binding energies of the PE(N)s, normalized to the exciton Rydberg energy, agree well with those of silicon, suggesting the universality of the phenomena.
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