Density dependence of mobility in a high quality Carbon-doped GaAs two-dimensional hole system

Two-dimensional hole systems (2DHSs) in GaAs/AlGaAs heterostructures offer a unique platform for the study of the concomitance of strong Coulomb interactions and spin-orbit coupling. Recent advances in the growth by molecular beam epitaxy of Carbon-doped 2DHS in (001) oriented GaAs heterostructures have resulted in a substantial increase in the achievable low temperature mobility. Here we report on a systematic study of mobility in a series of high quality Carbon-doped (001) GaAs 2DHS samples. Several samples consisting of 16{\%} AlGaAs barriers and 20nm GaAs quantum wells where grown with varying doping profiles to investigate the density dependence of mobility. Using an 80nm setback, a low temperature (T$\sim $50mK) mobility of 2.6x10$^{6}$cm$^{2}$/Vs at a density p=6.2x10$^{10}$cm$^{-2}$ was observed. Surprisingly, samples with similar structural design but with a higher as-grown 2D density of 1x10$^{11}$cm$^{-2}$ displayed a reduced mobility of 2.0x10$^{6}$cm$^{2}$/Vs. This behavior is distinct from that observed in high mobility two-dimensional electrons. In order to better understand the mechanisms influencing mobility in our 2DHSs we have studied the density dependence of mobility in a single sample using a backgate to modulate the density from 2x10$^{10}$cm$^{-2}$ to 1x10$^{11}$cm$^{-2}$.