Thermopower measurements of the coupling of phonons to electrons and composite fermions

The thermopower of electrons at zero magnetic field and composite fermions (CF’s) at high fields in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ heterojunctions has been measured in the temperature range 0.1–1.2 K. In both cases the data are completely consistent with phonon drag being the only visible contribution. The results have been used to evaluate the phonon-limited mobility of electrons and CF’s as a function of temperature. The electron mobility is in good agreement with calculation and with previous results deduced directly from the resistivity, but the CF mobility is not. We have previously reported that the thermopowers at filling factors $\nu =\frac{3}{2}$ and $\frac{1}{2}$ are identical. New data at fields up to 30 T show that this is also true for $\nu =\frac{3}{4}$ and $\frac{1}{4}$. The effect of the substrate crystallographic orientation on phonon drag thermopower is reported.