Tuning of the spin-orbit interaction and resistance in two-dimensional GaAs holes via strain

We report direct measurements, via the Fourier analysis of the Shubnikov-de Hass oscillations, of the spin-orbit interaction induced spin-splitting in modulation-doped GaAs two-dimensional hole systems as a function of strain applied in the sample plane. The data reveal a remarkably strong dependence of the spin-splitting on strain, with up to about 20{\%} enhancement of the splitting upon the application of only about 2x10$^{-4}$ strain. The results are in very good agreement with our numerical calculations of the strain-induced spin-splitting. We also show a remarkable dependence of the anisotropy of the heavy hole band on strain. Its manifestation as a change of resistance with strain implies the use of GaAs 2D holes as a sensitive piezo-resistance sensor at low temperatures.