Phonon spectroscopy of the electron-hole liquid in germanium

Abstract

The absorption of phonons by the electron-hole liquid (EHL) in semiconductors has proven to be the principal process causing macroscopic transport of droplets of this Fermi fluid. A characterization of the phonon absorption for frequencies of several hundred gigahertz promises to elucidate this "phonon wind" transport mechanism as well as test the basic theory of deformation potential scattering within a degenerate Fermi liquid. Central predictions of this theory are an absorption rate which increases linearly with frequency at low frequencies and a transparency for phonon wave vectors greater than $2k_F$, where $k_F$ is the Fermi wave vector of the liquid. We have adapted the standard deformation potential theory to the case in which the phonon energies are comparable to the Fermi energy and have calculated the frequency and angle dependences of the phonon absorption by electron-hole liquid in Ge. The sharpness and position of the $2k_F$ cutoffs depend upon propagation direction and phonon polarization. Using the method of tunnel-junction phonon spectroscopy, we have measured the absorption of monochromatic phonons by electron-hole liquid over the frequency range 150-500 GHz. We concentrated on longitudinal phonons with $\overrightarrow{\mathrm{q}}\parallel 〈111〉$, the long axis of an electron energy ellipsoid. By applying an appropriate uniaxial stress to the crystal we were able to vary the population of this valley, thereby continuously "tuning" the predicted $2k_F$ cutoff over a factor of about 4. The resulting absorption spectra agreed with theoretical predictions, displaying for the first time the $2k_F$ cutoff for this Fermi liquid. To determine the absolute phonon absorption length in EHL, we used a luminescence-imaging method to calibrate the volume of liquid in the phonon path. Our measured deformation potential is smaller than that obtained for free electrons in Ge via cyclotron resonance. We interpret this reduction in electron-phonon interaction strength as due to screening within the electron-hole liquid. This interpretation is consistent with a recent theoretical calculation.