Magnetoluminescence of the electron-hole liquid in germanium

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Abstract
We report photoluminescence measurements on the electron-hole liquid (EHL) in germanium in magnetic fields up to 19 T (190 kG). The line shape of the luminescence spectra for allowed (LA) as well as forbidden (TA) transitions could be fitted theoretically taking into account the detailed structure of the conduction and valence bands in a magnetic field. All details of the experimental line shape, including their polarization properties, are well reproduced by their theoretical counterparts over the entire field range. The low-energy tail of the EHL spectra could be described quantitatively by an energy-dependent quasiparticle lifetime. This line-shape analysis yielded the field dependence of the important parameters of the condensed state: equilibrium density, ground-state energy, and work function. It was found that there exists an enhancement of the carrier masses of about 10%. The sum of the exchange and correlation part of the ground-state energy turned out to be only weakly field dependent. Therefore a simple model is proposed which allows the calculation of the field dependence of the basic EHL parameters in an approximate way. The relative intensities of the TA- and LA-phonon replicas are quantitatively described over a large region of magnetic-field strength which confirms earlier findings on the nature of the electron-phonon matrix elements involved. No evidence for a field-induced transition from electron-hole droplets to electron-hole fibers, as predicted theoretically, has been found in our high-field optical experiments.