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.

arXiv comment9 pages, 22 figures

References in corpus (15)

• Electric Dipole Spin Resonance for Heavy Holes in Quantum Dots
• Highly anisotropic g-factor of two-dimensional hole systems
• Zeeman splitting in ballistic hole quantum wires
• Spin Orientation of Holes in Quantum Wells
• Topological Insulating States in Laterally Patterned Ordinary Semiconductors
• Observation of orientation- and $k$-dependent Zeeman spin-splitting in hole quantum wires on (100)-oriented AlGaAs/GaAs heterostructures
• Observation of the Kondo Effect in a Spin-3/2 Hole Quantum Dot
• Anisotropic modification of the effective hole $g$-factor by electrostatic confinement
• Magnetic field induced valence band mixing in [111] grown semiconductor quantum dots
• 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
• Using a tunable quantum wire to measure the large out-of-plane spin splitting of quasi two-dimensional holes in a GaAs nanostructure
• Hole spin dynamics and hole $g$ factor anisotropy in coupled quantum well systems
• Anisotropic Zeeman splitting in p-type GaAs quantum point contacts
• In-plane magnetic field effect on hole cyclotron mass and $g_z$ factor in high-mobility SiGe/Ge/SiGe structures

Cited by in corpus (22)

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• Generating a topological anomalous Hall effect in a non-magnetic conductor
• Electrical control of the $g$-tensor of a single hole in a silicon MOS quantum dot
• Ballistic one-dimensional holes with strong g-factor anisotropy in germanium
• Electrical control of the Zeeman spin splitting in two-dimensional hole systems
• Electrical operation of planar Ge hole spin qubits in an in-plane magnetic field
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Mechanisms for strong anisotropy of in-plane g-factors in hole based quantum point contacts
• 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
• G-factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field
• Determination of spin-orbit interaction in semiconductor nanostructures via non-linear transport
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Tuning the topological insulator states of artificial graphene
• Signatures of quantum mechanical Zeeman effect in classical transport due to topological properties of two-dimensional spin-3/2 holes
• Asymmetric $g$ tensor in low-symmetry two-dimensional hole systems
• Non-linear anomalous Hall effect of two-dimensional spin-3/2 heavy holes
• Zeeman spin-orbit coupling in antiferromagnetic conductors
• Interference in spin-orbit coupled transverse magnetic focusing; emergent phase due to in-plane magnetic fields
• 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