Dimensional reduction of the Luttinger Hamiltonian and g-factors of holes in symmetric two-dimensional semiconductor heterostructures

Abstract

The spin-orbit interaction of holes in zinc-blende semiconductors is much stronger than that of electrons. This makes the hole systems very attractive for possible spintronics applications. In three dimensions (3D) dynamics of holes is described by well known Luttinger Hamiltonian. However, most of recent spintronics applications are related to two dimensional heterostructures where dynamics in one direction is frozen due to quantum confinement. The confinement results in dimensional reduction of the Luttinger Hamiltonian, 3D ->2D. Due to interplay of the spin-orbit interaction, the external magnetic field, and the lateral gate potential imposed on the heterostructure the reduction is highly nontrivial and not known. In the present work we perform the reduction and hence derive the general effective Hamiltonian which describes spintronics effects in symmetric two-dimensional (2D) heterostructures. In particular, we do the following, (i) derive the spin-orbit interaction and the Darwin interaction related to the lateral gate potential, (ii) determine the momentum dependent out-of-plane g-factor, (iii) point out that there are two independent in-plane g-factors, (iv) determine momentum dependencies of the in-plane g-factors.

9 pages, 22 figures

References in corpus (8)

• Electric Dipole Spin Resonance for Heavy Holes in Quantum Dots
• Zeeman splitting in ballistic hole quantum wires
• Spin Orientation of Holes in Quantum Wells
• Anisotropic modification of the effective hole $g$-factor by electrostatic confinement
• Characterization of spin-orbit interactions of GaAs heavy holes using a quantum point contact
• Interplay between one-dimensional confinement and crystallographic anisotropy in ballistic hole quantum wires
• Hole spin dynamics and hole $g$ factor anisotropy in coupled quantum well systems
• In-plane magnetic field effect on hole cyclotron mass and $g_z$ factor in high-mobility SiGe/Ge/SiGe structures

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• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Cavity Control over Heavy-Hole Spin Qubits in Inversion-Symmetric Crystals
• Exchange interaction of hole-spin qubits in double quantum dots in highly anisotropic semiconductors
• Determination of spin-orbit interaction in semiconductor nanostructures via non-linear transport
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Non-linear anomalous Hall effect of two-dimensional spin-3/2 heavy holes
• Correlated physics in an artificial triangular anti-dot lattice
• Weak localization in p-type heterostructures in the presence of parallel magnetic field
• Transverse magnetic focusing in two-dimensional hole gases