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

TL;DR

This paper resolves Rashba-split heavy-hole dispersions in undoped (100) GaAs 2D hole gases by employing low-field SdH analysis in high-mobility, accumulation-mode dopant-free devices. By Fourier-analyzing the beating patterns in SdH oscillations, the authors extract branch-resolved carrier densities and effective masses (HH$-$ mass $m_1 \approx 0.34\,m_e$ is nearly density-independent, while HH$+$ mass $m_2$ grows with density and is strongly non-parabolic), enabling a transport-based reconstruction of the HH$-$ and HH$+$ dispersions and the spin-orbit splitting $\Delta_{\text{HH}}=E_1-E_2$. The experiments reach high Rashba spin polarization ($\Delta p/p$ up to $\sim 0.36$) and densities from $0.76$ to $1.9\times 10^{15}\ \mathrm{m^{-2}}$, with masses larger than Luttinger-model predictions by a factor of about two, suggesting substantial many-body renormalization. Overall, the work provides a robust, parameter-free empirical mapping of non-parabolic heavy-hole bands in strongly asymmetric confinement and establishes a benchmark for interaction-aware theories of hole spin–orbit physics in GaAs and related materials.

Abstract

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 $Δ_\text{HH}$ 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.

Figures (33)

• Figure 1: Schematic energy dispersion diagram of the conduction band (CB) and valence band (VB) at small wave vector $k_x$ values for a direct bandgap semiconductor: (a) bulk (3D), (b) symmetric quantum well (2D), and (c) asymmetric quantum well (QW). Values of the orbital angular momentum $L$, the total angular momentum $J$, and the projection $m_j$ of the latter for each subband are indicated. (d) Enlarged energy dispersion diagram for the LH and HH subbands versus in-plane $k_x$ values, illustrating the anticrossing of HH$-$/LH$+$ when taking into account LH/HH mixing. The HH$+$ and HH$-$ dispersions are shown near a Fermi energy $E_F$ typically observed in experiments.
• Figure 2: Layer structure of the six GaAs/AlGaAs heterostructures reported here (not to scale). None of the layers are intentionally doped. The red dashed line (box) indicates the location of the 2DHG in a single heterojunction (quantum well).
• Figure 3: High-field SdH oscillations in sample K at $T=100$ mK for hole densities: (a) $p_{2d} = 2.27 \times 10^{15}$/m$^2$ and (b) $p_{2d} = 1.73 \times 10^{15}$/m$^2$. The latter density corresponds to the mobility peak, 84 m$^2$/Vs, for this sample. In both panels, many fractional quantum Hall states can be observed at filling factors $\nu=$ 5/3, 4/3, 2/3, 3/5, and 4/7, easily identifiable by their quantum Hall plateau (not shown). Even at the highest $p_{2d}$, the high-field SdH oscillation at $\nu=$ 2/3 reaches $\rho_{xx}=0$ Ω.
• Figure 4: High mobilities at $T<0.1$ K for samples listed in Table \ref{['tab:samples']}. Lines are guides to the eye. The mobility of all samples was measured at $B=50$ mT, except for samples K and M which were measured at $B \approx 10$ mT.
• Figure 5: (a) Hole and (b) electron mobilities in ambipolar Hall bars (samples A, B, and C) at $T=1.6$ K, as a function of gate dielectric. Lines are guides to the eye.