High-frequency transport in $p$-type $\mathrm{Si}∕{\mathrm{Si}}_{0.87}{\mathrm{Ge}}_{0.13}$ 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 $30–300\mathrm{MHz}$. For temperatures in the range $0.7<T<1.6\mathrm{K}$ and magnetic fields up to $7\mathrm{T}$, the SAW attenuation coefficient $\Gamma$ and velocity change $\Delta V∕V$ were found to oscillate with filling factor. Both the real ${\sigma }_1$ and imaginary ${\sigma }_2$ components of the high-frequency conductivity have been determined and compared with quasi-dc magnetoresistance measurements at temperatures down to $33\mathrm{mK}$. By analyzing the ratio of ${\sigma }_1$ to ${\sigma }_2$, carrier localization can be followed as a function of temperature and magnetic field. At $T=0.7\mathrm{K}$, the variations of $\Gamma$, $\Delta V∕V$, and ${\sigma }_1$ 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.

Figure 1

Layer scheme of the sample.

Figure 2

Resistivity components, in units of $h∕e^2$ at different temperatures.

Figure 3

Magnetic field dependence of $\Gamma$ and $\Delta V∕V$ with a SAW frequency of $30\mathrm{MHz}$ together with the dc resistivity components ${\rho }_{xx}$ and ${\rho }_{xy}$. All at $T=0.7\mathrm{K}.$

Figure 4

Magnetic field dependence of ${\sigma }_1$ (solid), ${\sigma }_2$ (dashed) at $f=30\mathrm{MHz}$, and ${\sigma }_{xx}^{\mathrm{dc}}$ (dotted); all at $T=0.7\mathrm{K}$.

Figure 5

Magnetic field dependences of the absorption coefficient $\Gamma$ at different frequences at $T=1\mathrm{K}$.

Figure 6

(a) Dependences of ${\sigma }_1$ on magnetic field $B$ at different rf-source powers, $T=0.7$, $f=30\mathrm{MHz}$; (b) ${\sigma }_1$ versus $B$ in the linear regime $(P\simeq 5\times {10}^{-6}\mathrm{W})$ at different temperatures, $f=30\mathrm{MHz}$.

Figure 7

(a) Dependence of ${\sigma }_1$ on the rf-source power $P$; (b) temperature variation of ${\sigma }_1$ in the linear regime. $f=30\mathrm{MHz}$, magnetic fields of $4.3\mathrm{T}$ (circles) and $2.9\mathrm{T}$ (stars) correspond to $\nu =2$ and 3, respectively. The lines are guides to the eye.

Figure 8

The energy losses rate per hole measured in acoustics $Q=\overline{Q}∕p$ plotted versus $T_c$. Lines are the fitting curves with $\gamma =5$ (dotted) and $\gamma =7$ (solid). Inset: dependence of $Q$ on $(T_c^{\gamma }-T^{\gamma })$. Lines are results of the linear fit.