Spin-orbit interactions in inversion-asymmetric 2D hole systems: a variational analysis

Abstract

We present an in-depth study of the spin-orbit (SO) interactions occurring in inversion-asymmetric two-dimensional hole gases at semiconductor heterointerfaces. We focus on common semiconductors such as GaAs, InAs, InSb, Ge, and Si. We develop a semi-analytical variational method to quantify SO interactions, accounting for both structure inversion asymmetry (SIA) and bulk inversion asymmetry (BIA). Under certain circumstances, using the Schrieffer-Wolff (SW) transformation, the dispersion of the ground state heavy hole subbands can be written as $E(k)=A{k}^2-B{k}^4\pm C{k}^3$ where $A$, $B$, and $C$ are material- and structure-dependent coefficients. We provide a simple method of calculating the parameters $A$, $B$, and $C$, yet demonstrate that the simple SW approximation leading to a SIA (Rashba) spin splitting $\propto k^3$ frequently breaks down. We determine the parameter regimes at which this happens for the materials above and discuss a convenient semi-analytical method to obtain the correct spin splitting, effective masses, Fermi level, and subband occupancy, together with their dependence on the charge density, dopant type, and dopant concentration for both inversion and accumulation layers. Our results are in good agreement with fully numerical calculations as well as with experimental findings. They suggest that a naive application of the simple cubic Rashba model is of limited use in common heterostructures, as well as quantum dots. Finally, we find that for the single heterojunctions studied here the magnitudes of BIA terms are always much smaller than those of SIA terms.

13 pages, 8 figures

References in corpus (15)

• Spin relaxation and decoherence of holes in quantum dots
• Electric Dipole Spin Resonance for Heavy Holes in Quantum Dots
• Dissipation effects in spin-Hall transport of electrons and holes
• Pauli Spin Blockade of Heavy Holes in a Silicon Double Quantum Dot
• Spin Hall effect of conserved current: Conditions for a nonzero spin Hall current
• Spin Orientation of Holes in Quantum Wells
• Generation of spin currents and spin densities in systems with reduced symmetry
• Electric-field dependent g-factor anisotropy in Ge-Si core-shell nanowire quantum dots
• Spin precession and alternating spin polarization in spin-3/2 hole systems
• On the nature of steady states of spin distributions in the presence of spin-orbit interactions
• Characterization of spin-orbit interactions of GaAs heavy holes using a quantum point contact
• Spin polarization decay in spin-1/2 and spin-3/2 systems
• Enhanced Rashba effect for hole states in a quantum dot
• Conserved Spin Quantity in Strained Hole Systems with Rashba and Dresselhaus Spin-Orbit Coupling
• Zitterbewegung of a heavy hole in presence of spin-orbit interactions

Cited by in corpus (57)

• The germanium quantum information route
• Ge hole spin qubit
• Ultrafast Hole Spin Qubit with Gate-Tunable Spin-Orbit Switch
• Ultrafast coherent control of a hole spin qubit in a germanium quantum dot
• Theory of Hole-Spin Qubits in Strained Germanium Quantum Dots
• Optimal operation points for ultrafast, highly coherent Ge hole spin-orbit qubits
• Generating a topological anomalous Hall effect in a non-magnetic conductor
• Hole spin driving by strain-induced spin-orbit interactions
• Single-shot readout of hole spins in Ge
• Observation of a cubic Rashba effect in the surface spin structure of rare-earth ternary materials
• A natural heavy-hole flopping mode qubit in germanium
• Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband $\vec{k}\cdot \vec{p}$ method
• Hole spin manipulation in inhomogeneous and non-separable electric fields
• Longitudinal and transverse electric field manipulation of hole spin-orbit qubits in one-dimensional channels
• Strong influence of spin-orbit coupling on magnetotransport in two-dimensional hole systems
• Spin blockade as a probe of Zeeman interactions in hole quantum dots
• Electrical control of the Zeeman spin splitting in two-dimensional hole systems
• Emergence of the strong tunable linear Rashba spin-orbit coupling of two-dimensional hole gases in semiconductor quantum
• Electrical operation of planar Ge hole spin qubits in an in-plane magnetic field
• Quantum control of hole spin qubits in double quantum dots
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Detection and control of spin-orbit interactions in a GaAs hole quantum point contact
• Linear-in-momentum spin orbit interactions in planar Ge/GeSi heterostructures and spin qubits
• The emergent linear Rashba spin-orbit coupling offering the fast manipulation of hole-spin qubits in germanium
• Geometry of the dephasing sweet spots of spin-orbit qubits
• Majorana zero modes in gate-defined germanium hole nanowires
• Majorana bound states in germanium Josephson junctions via phase control
• Pseudospin-electric coupling for holes beyond the envelope-function approximation
• Determination of spin-orbit interaction in semiconductor nanostructures via non-linear transport
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Hole spin in tunable Ge hut wire double quantum dot
• Gate-defined Two-dimensional Hole and Electron Systems in an Undoped InSb Quantum Well
• Polarization and third-order Hall effect in III-V semiconductor heterojunctions
• An upper and lower bound to the orientation-dependent linear Rashba spin-orbit coupling of two-dimensional hole gases in semiconductor quantum wells
• Non-linear anomalous Hall effect of two-dimensional spin-3/2 heavy holes
• Dephasing of planar Ge hole spin qubits due to 1/$\text{f}$ charge noise
• Spin splitting in low-symmetry quantum wells beyond Rashba and Dresselhaus terms
• Probing details of spin--orbit coupling through Pauli spin blockade
• Effects of spin-orbit coupling and in-plane Zeeman fields on the critical current in two-dimensional hole gas SNS junctions
• A spinless spin qubit
• Phase diagram of the interacting persistent spin-helix state
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Depletion-mode Quantum Dots in Intrinsic Silicon
• Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire
• Current-induced spin polarisation in Rashba-Dresselhaus systems under different point groups
• Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger-Kohn Hamiltonian
• Bulk inversion asymmetry induced magnetogyrotropic reflection from quantum wells
• Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire
• Spin-orbit-induced hole spin relaxation in a quantum dot molecule: the effect of $s$-$p$ coupling
• Effect of disorder and strain on the operation of planar Ge hole spin qubits
• Variability of hole spin qubits in planar Germanium
• Photodriven germanium hole qubit
• Role of anisotropic confining potential and elliptical driving in dynamics of a Ge hole qubit
• Nested Fermi surfaces and correlated electronic phases in hole-doped semiconductor quantum wells
• Dressed basis sets for the modeling of exchange interactions in double quantum dots
• Transverse magnetic focusing in two-dimensional hole gases
• Switchable spin-photon coupling with hole spins in single-quantum dots