High-frequency transport in p -type Si/ Si 0.87 Ge 0.13 heterostructures studied with surface acoustic waves in the quantum Hall regime

The interaction of surface acoustic waves (SAWs) with $p$-type $\mathrm{Si}∕{\mathrm{Si}}_{0.87}{\mathrm{Ge}}_{0.13}$ heterostructures has been studied for SAW frequencies of $30\char21{}300\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. For temperatures in the range $0.7lTl1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and magnetic fields up to $7\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, the SAW attenuation coefficient $\ensuremath{\Gamma}$ and velocity change $\ensuremath{\Delta}V∕V$ were found to oscillate with filling factor. Both the real ${\ensuremath{\sigma}}_{1}$ and imaginary ${\ensuremath{\sigma}}_{2}$ components of the high-frequency conductivity have been determined and compared with quasi-dc magnetoresistance measurements at temperatures down to $33\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. By analyzing the ratio of ${\ensuremath{\sigma}}_{1}$ to ${\ensuremath{\sigma}}_{2}$, carrier localization can be followed as a function of temperature and magnetic field. At $T=0.7\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the variations of $\ensuremath{\Gamma}$, $\ensuremath{\Delta}V∕V$, and ${\ensuremath{\sigma}}_{1}$ with SAW intensity have been studied and can be explained by heating of the two-dimensional hole gas by the SAW electric field. Energy relaxation is found to be dominated by acoustic phonon deformation potential scattering with weak screening.