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 $Δ_\text{HH}$ 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.

💡 Research Summary

This paper presents a comprehensive experimental investigation of Rashba spin‑orbit splitting and effective‑mass renormalization in undoped (100) GaAs/AlGaAs single‑heterojunction two‑dimensional hole gases (2DHGs). The authors fabricate accumulation‑mode field‑effect transistors (SISFET/HIGFET) that are completely dopant‑free, allowing them to apply large out‑of‑plane electric fields up to 26 kV cm⁻¹ while preserving exceptionally high mobilities (up to 84 m² V⁻¹ s⁻¹). Under these conditions the heavy‑hole (HH) subband is split into two Rashba‑polarized branches, denoted HH⁻ (spin‑down) and HH⁺ (spin‑up), with a spin‑orbit polarization as large as 36 %—the highest reported for GaAs 2DHGs in either single‑heterojunction or quantum‑well geometries.

Low‑field magnetotransport (B < 1 T) is used to record Shubnikov‑de Haas (SdH) oscillations at temperatures down to 30 mK. Fourier‑transform (FT) analysis of the SdH signal reveals two distinct frequencies f₋ and f₊, directly proportional to the carrier densities p₋ and p₊ of the HH⁻ and HH⁺ subbands. By measuring the temperature dependence of the FT amplitudes A₋(T) and A₊(T) and fitting them with the Lifshitz‑Kosevich formula, the authors extract branch‑resolved effective masses m*₋ and m*₊ over the same magnetic‑field window (0.2–0.8 T). This method circumvents the usual assumption of a single parabolic band and is therefore applicable to strongly non‑parabolic systems.

The experimental results show that m*₋ ≈ 0.34 mₑ and remains essentially constant across the investigated density range p = 0.76–1.9 × 10¹⁵ m⁻². This indicates that the HH⁻ branch retains a nearly parabolic dispersion below the first light‑hole (LH⁺)/HH⁻ anticrossing, and its Fermi wave vector can be obtained from the simple relation k_F₋ = √(2πp₋). In contrast, m*₊ increases markedly with density, ranging from ~0.5 mₑ at low p to ~0.9 mₑ at the highest p, reflecting strong HH–LH mixing and a highly non‑parabolic HH⁺ dispersion. By assuming a common Fermi energy for both branches, the authors map the HH⁺ dispersion E₊(k) and directly determine the Rashba spin‑orbit splitting energy Δ_HH(k) as a function of in‑plane wave vector.

To interpret the data, parameter‑free calculations based on the 4 × 4 Luttinger‑Kohn Hamiltonian are performed. The theoretical trends for both effective masses and Δ_HH(k) are reproduced qualitatively, but the calculated masses are systematically smaller by a factor of ≈2. This discrepancy points to a many‑body renormalization of the heavy‑hole mass in the strongly asymmetric confinement regime, an effect not captured by the single‑particle Luttinger model. The authors discuss how this many‑body enhancement may arise from exchange‑correlation interactions that become pronounced under large electric fields and high carrier densities.

The paper also resolves inconsistencies reported in earlier transport studies of (100) GaAs 2DHGs, which showed conflicting mass values and magnetic‑field dependencies. By carefully delineating the magnetic‑field windows where the beating pattern of the SdH oscillations is reliable, the authors demonstrate that neither effective mass exhibits any measurable B‑dependence for B < 1 T, contrary to some previous reports. Moreover, the use of a single‑heterojunction geometry, rather than a quantum well, enables the observation of the highest mobilities together with the strongest spin‑orbit splitting reported to date.

Beyond the immediate GaAs system, the methodology—combining dopant‑free accumulation devices, low‑field SdH beating analysis, and branch‑resolved mass extraction—provides a general framework for probing non‑parabolic, spin‑split bands in other material platforms such as Ge, InAs, or InSb. The empirical dispersion relations derived here can be employed in device modeling for spin‑tronic applications, hole‑based qubits, and spin‑to‑photon conversion schemes, where precise knowledge of effective mass and spin‑orbit splitting is crucial.

In summary, the authors deliver a detailed, transport‑based mapping of the Rashba‑split heavy‑hole dispersions in a highly asymmetric GaAs 2DHG, reveal a substantial many‑body enhancement of the heavy‑hole mass, and establish a robust experimental protocol for extracting spin‑orbit‑split band parameters in low‑dimensional semiconductor systems.