Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire

Abstract

Quasi-one-dimensional hole gas is achievable in a semiconductor Ge nanowire. The lowest two subband dispersions of the hole gas are just two shifted parabolic curves with an anticrossing at $k_z=0$. This peculiar low-energy subband structure manifests the existence of a strong `spin' (pseudo spin)-orbit coupling. Based on the Luttinger-Kohn Hamiltonian in the axial approximation, we show two sets of combined dispersions that not only isolated from each other but also with strong `spin'-orbit coupling are obtainable in the presence of strong magnetic field. Realistic calculations are performed for three representative nanowire growth directions [001], [111], and [110]. These results are further confirmed via constructing the low-energy effective Hamiltonian of the hole gas. We also calculate the external electric field induced spin splitting for comparison with the magnetic field induced spin splitting.

17 pages, 17 figures. Published version

References in corpus (24)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• One-Dimensional Hole Gas in Germanium/Silicon Nanowire Heterostructures
• Heavy hole states in Germanium hut wires
• Majorana Fermions in Ge/Si Hole Nanowires
• Tunable g factor and phonon-mediated hole spin relaxation in Ge/Si nanowire quantum dots
• Spin-3/2 physics of semiconductor hole nanowires: Valence-band mixing and tunable interplay between bulk-material and orbital bound-state spin splittings
• Simple model for electrical hole spin manipulation in semiconductor quantum dots: Impact of dot material and orientation
• Anisotropic Pauli spin blockade in hole quantum dots
• Hole Spin Qubits in Ge Nanowire Quantum Dots: Interplay of Orbital Magnetic Field, Strain, and Growth Direction
• Large variations in the hole spin splitting of quantum-wire subband edges
• Hole spin qubits in thin curved quantum wells
• Acoustic phonons and strain in core/shell nanowires
• Highly tuneable hole quantum dots in Ge-Si core-shell nanowires
• Enhanced orbital magnetic field effects in Ge hole nanowires
• Majorana zero modes in gate-defined germanium hole nanowires
• Lande-like formula for the g factors of hole-nanowire subband edges
• Hole spin relaxation in $p$-type (111) GaAs quantum wells
• Microscopic analysis of proximity-induced superconductivity and metallization effects in superconductor-germanium hole nanowires
• Band structure of n- and p-doped core-shell nanowires
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Electrical manipulation of a hole `spin'-orbit qubit in nanowire quantum dot: the nontrivial magnetic field effects
• Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire
• Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger-Kohn Hamiltonian
• Spin-photon interaction in a nanowire quantum dot with asymmetrical confining potential

Cited by in corpus (2)

• Low-energy effective Hamiltonian and end states of an inverted HgTe nanowire
• Band inversion transition in HgTe nanowire grown along the [001] direction