Enhanced effective masses, spin-orbit polarization, and dispersion relations in 2D hole gases under strongly asymmetric confinement

The dispersion of Rashba-split heavy-hole subbands in GaAs two-dimensional hole gases (2DHGs) is difficult to access experimentally because strong heavy-hole-light-hole mixing produces non-parabolicity and breaks the usual correspondence between carrier density and Fermi wave vector. Here we use low-field magnetotransport (B < 1 T) to reconstruct the dispersions of the two spin-orbit-split heavy-hole branches (HH-, HH+) in undoped (100) GaAs/AlGaAs single heterojunction 2DHGs operated in an accumulation-mode field-effect geometry. The dopant-free devices sustain out-of-plane electric fields up to 26 kV/cm while maintaining mobilities up to 84 m$^2$/Vs and exhibiting a spin-orbit polarization as large as 36%. Fourier analysis of Shubnikov-de Haas (SdH) oscillations resolves the individual HH-/HH+ subband densities; fitting the temperature dependence of the corresponding Fourier amplitudes yields both branch-resolved SdH effective masses over the same magnetic field window. SdH regimes in which reliable subband parameters can be extracted are delineated. Over 2DHG densities (0.76-1.9) $\times$ 10$^{15}$ /m$^2$, the HH- mass is nearly density independent ($\approx 0.34m_e$), implying a near-parabolic HH- dispersion below the first LH+/HH- anticrossing, whereas HH+ exhibits strong non-parabolicity with an effective mass that increases with density. Combining the extracted dispersions yields a transport-based determination of the spin-orbit splitting energy $\Delta_\text{HH}$ between HH and HH+ as a function of in-plane wave vector. Parameter-free Luttinger-model calculations reproduce the qualitative trends but underestimate both masses by a common factor $\approx$ 2, suggesting a many-body renormalization of the heavy-hole mass in this strongly asymmetric regime.