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.

arXiv comment9 pages, 7 figures

References in corpus (22)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• 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
• Band structure of semimagnetic Hg1-yMnyTe quantum wells
• 3D massless Kane fermions observed in a zinc-blende crystal
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Strong Spin-Orbit Interaction and Helical Hole States in Ge/Si Nanowires
• Split Dirac cones in HgTe/CdTe quantum wells due to symmetry-enforced level anticrossing at interfaces
• Spin-3/2 physics of semiconductor hole nanowires: Valence-band mixing and tunable interplay between bulk-material and orbital bound-state spin splittings
• Robust Level Coincidences in the Subband Structure of Quasi 2D Systems
• Topological states in superlattices of HgTe-class materials for engineering three-dimensional flat bands
• CdTe-HgTe core-shell nanowire growth controlled by RHEED
• 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
• Cross-section geometry effects in the subband structure and spin-related properties of a HgTe/CdTe nanowire
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• 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