Phonon Emission and Absorption Experiments in the Quantum-Hall Regime
The absorption and emission of phonons by a two-dimensional electron gas (2DEG) has been studied in a quantizing magnetic field. The 2DEG was formed at the interface of a GaAs/AlxGa1-x As heterojunction. Absorption experiments were done by creating acoustic phonons by heating the substrate locally with a focused laser beam. The phonons travelled ballistically through the crystal and were partially absorbed by the 2DEG. This led to a transfer of momentum into the 2DEG (phonon-drag effect) resulting in phonon-induced voltages and currents. These quantities gave detailed information about the interaction between acoustic phonons and the 2DEG as a function of both the incident angle of the absorbed phonons and the magnetic field. We observed that the absolute intensity of the phonon-drag signal was oscillating in phase with the Shubnikov de-Haas oscillations while the angular dependence did not change in the field. These results could be explained with a simple microscopic theory of the electron-phonon-interaction (EPI) together with a macroscopic model for the response of the 2DEG on the absorption of ballistic phonons.
The spatial distribution of the emission of phonons was studied using the fountain-pressure technique. It was found that 2DEG samples in a strong magnetic field dissipate phonons only in areas where a strong electric field is present. This is the case at the current entry and exit points of the contacts and, in the case of the break-down of the quantum-Hall effect, at filaments in the interior of the samples.
of the substrate material. The matrix element of this interaction contains an overlap integral of the respective wavefunctions of the electron and the phonons. In zero magnetic field this leads to the conservation of the in-plane momentum and of the energy. The interaction strength follows from the symmetry of the phonon strains and from parameters like the deformation potentials and the piezoelectric interactions.
The situation is less clear if magnetic field is applied which is strong enough to quantize the electron-energy spectrum in Landau-levels. The electron wave functions then become localized. Thus the in-plane momentum conservation rule no longer exists and the matrix element will take a more complicated form. A further complication arises because the current and electrostatic-potential distributions are no longer homogeneous over the sample surface.
In this contribution we report on our recent results about the phonon absorption and emission by a 2DEG in a strong magnetic field. The first ones were done by exposing a 2DEG sample to a flux of ballistic phonons. The phonon absorption strength was measured by observing the phonon-drag effect. In the case of the phonon emission we concentrated on the question of the spatial distribution of the emission processes. This was done by utilizing the fountain-pressure of superfluid helium.  Alternative approaches to study the elctron phonon interaction are being used by the group in Nottingham. Their work is being reviewed by Challis and Kent.
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