Spin-orbit coupling in wurtzite quantum wells

Abstract

Effective spin-orbit (SO) Hamiltonians for conduction electrons in wurtzite heterostructures are lacking in the literature, in contrast to zincblende structures. Here we address this issue by deriving such an effective Hamiltonian valid for quantum wells, wires, and dots with arbitrary confining potentials and external magnetic fields. We start from an 8$\times$8 Kane model accounting for the $s$--$p_z$ orbital mixing important to wurtzite structures, but absent in zincblende, and apply both quasi-degenerate perturbation theory (Löwdin partitioning) and the folding down approach to derive an effective 2$\times$2 electron Hamiltonian. We obtain the usual $k$-linear Rashba term arising from the structural inversion asymmetry of the wells and, differently from zincblende structures, a bulk Rashba-type term induced by the inversion asymmetry of the wurtzite lattice. We also find linear- and cubic-in-momentum Dresselhaus contributions. Both the bulk Rashba-type term and the Dresselhaus terms originate exclusively from the admixture of $s$- and $p_z$-like states in wurtzites structures. Interestingly, in these systems the linear Rashba and the Dresselhaus terms have the same symmetry and can in principle cancel each other out completely, thus making the spin a conserved quantity. We determine the intrasubband (intersubband) Rashba ${\alpha }_{\nu }$ ($\eta$) and linear Dresselhaus ${\beta }_{\nu }$ ($\Gamma$) SO strengths of GaN/AlGaN single and double wells with one and two occupied subbands ($\nu =1,2$). We believe our general effective Hamiltonian for electrons in wurtzite heterostructures put forward here, should stimulate additional theoretical works on wurtzite quantum wells, wires, and dots with variously defined geometries and external magnetic fields.

25 pages, 8 figures; for a more complete abstract than that shown here in Metadata which has a length limit, see the manuscript

References in corpus (31)

• Spintronics: Fundamentals and applications
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Majorana fermions in a tunable semiconductor device
• Non-ballistic spin field-effect transistor
• An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System
• Emergence of the persistent spin helix in semiconductor quantum wells
• Spin dynamics in semiconductors
• Direct mapping of the formation of a persistent spin helix: Supplementary information
• Spin-orbit interaction in symmetric wells with two subbands
• Intersubband-induced spin-orbit interaction in quantum wells
• Spin orbit coupling in bulk ZnO and GaN
• Stretchable persistent spin helices in GaAs quantum wells
• Large Bychkov-Rashba spin-orbit coupling in high-mobility GaN/AlGaN heterostructures
• First-principles studies of orbital and spin-orbit properties of GaAs, GaSb, InAs, and InSb zinc-blende and wurtzite semiconductors
• Demonstration of Rashba spin splitting in GaN-based heterostructures
• Realistic multiband k.p approach from ab initio and spin-orbit coupling effects of InAs and InP in wurtzite phase
• Weak antilocalization and zero-field electron spin splitting in AlGaN/AlN/GaN heterostructures with a polarization induced two-dimensional electron gas
• Spin-orbit interaction in GaAs wells: From one to two subbands
• Persistent Skyrmion Lattice of Noninteracting Electrons with Spin-Orbit Coupling
• Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation
• Polarization-induced Rashba spin-orbit coupling in structurally symmetric III-Nitride quantum wells
• Anomalous k-dependent spin splitting in wurtzite AlxGa1-xN/GaN heterostructures
• Experimental determination of Rashba spin-orbit coupling in wurtzite $n$-GaN:Si
• Excitons in the wurtzite AlGaN/GaN quantum-well heterostructures
• Prediction of extremely long electron spin lifetimes at room temperature in wurtzite semiconductor quantum wells
• Rashba field in GaN
• Spin-relaxation time in the impurity band of wurtzite semiconductors

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