Subband structure of a cylindrical HgTe nanowire: transition from normal type to inverted type

Abstract

Based on the $6\times 6$ Kane model in the spherical approximation, both the electron and the hole subband dispersions in a cylindrical HgTe nanowire are calculated using analytical method. The transcendental equations determining the subband energies in the nanowire are analytically derived by utilizing both the total angular momentum conservation and the hard wall boundary condition. We show there exists topological band transition in the HgTe nanowire, very similar to that demonstrated in a HgTe quantum well. Via tuning the radius of the nanowire, we find there is a gap-closing-and-reopening transition in the subband structure. When the radius is larger than the critical radius $R_{\mathrm{c}}\approx 3.2$ nm, the HgTe nanowire is in the inverted regime.

9 pages, 7 figures

References in corpus (12)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Spin-3/2 physics of semiconductor hole nanowires: Valence-band mixing and tunable interplay between bulk-material and orbital bound-state spin splittings
• Topological states in superlattices of HgTe-class materials for engineering three-dimensional flat bands
• Spin-orbit insulating phase in SnTe cubic nanowires: consequences on the topological surface states
• Revisiting the physical origin and nature of surface states in inverted-band semiconductors
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Cross-section geometry effects in the subband structure and spin-related properties of a HgTe/CdTe nanowire
• Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger-Kohn Hamiltonian

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