Energy relaxation rate of 2D hole gas in GaAs/InGaAs/GaAs quantum well within wide range of conductivitiy

The nonohmic conductivity of 2D hole gas (2DHG) in single $GaAsIn_{0.2}Ga_{0.8}AsGaAs$ quantum well structures within the temperature range of 1.4 - 4.2K, the carrier's densities $p=(1.5-8)\cdot10^{15}m^{-2}$ and a wide range of conductivities $(10^{-4}-100)G_0$ ($G_0=e^2/\pi\,h$) was investigated. It was shown that at conductivity $\sigma>G_0$ the energy relaxation rate $P(T_h,T_L)$ is well described by the conventional theory (P.J. Price J. Appl. Phys. 53, 6863 (1982)), which takes into account scattering on acoustic phonons with both piezoelectric and deformational potential coupling to holes. At the conductivity range $0.01G_0<\sigma<G_0$ energy the relaxation rate significantly deviates down from the theoretical value. The analysis of $\frac{dP}{d\sigma}$ at different lattice temperature $T_L$ shows that this deviation does not result from crossover to the hopping conductivity, which occurs at $\sigma<10^{-2}$, but from the Pippard ineffectiveness.
Comment: 13 pages, 6 figures