Low-field magnetoresistance in GaAs two-dimensional holes

We report low-field magnetotransport data in two-dimensional hole systems in $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures and quantum wells, in a large density range $2.5\times {10}^{10}<~p<~4.0\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2},$ with a primary focus on samples grown on (311)A GaAs substrates. At high densities, $p\gtrsim 1\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2},$ we observe a remarkably strong positive magnetoresistance. It appears in samples with an anisotropic in-plane mobility and predominantly along the low-mobility direction, and is strongly dependent on the perpendicular electric field and the resulting spin-orbit interaction-induced spin-subband population difference. A careful examination of the data reveals that the magnetoresistance must result from a combination of factors including the presence of two spin subbands, a corrugated quantum-well interface which leads to the mobility anisotropy, and possibly weak antilocalization. None of these factors can alone account for the observed positive magnetoresistance. We also present the evolution of the data with density: the magnitude of the positive magnetoresistance decreases with decreasing density until, at the lowest density studied $(p=2.5\mathrm{}\times {10}^{10}\hspace{0.5em}{\mathrm{cm}}^{-2}),$ it vanishes and is replaced by a weak negative magnetoresistance.