Band inversion transition in HgTe nanowire grown along the [001] direction

Abstract

The low-energy effective Hamiltonian of a cylindrical HgTe nanowire grown along the [001] crystallographic direction is constructed by using the perturbation theory. Both the anisotropic term and the bulk inversion asymmetry term of the Kane model are taken into account. Although the anisotropic term has converted the crossing between the $E_1$ and $H_1$ subbands into an anticrossing at $k_{z}R=0$, the gap-closing-and-reopening transition in the subband structure can still occur at finite wave vectors $k_{z}R\approx \pm 0.24$ for critical nanowire radius $R\approx 3.45$ nm. The bulk inversion asymmetry does not contribute to the low-energy effective Hamiltonian, i.e., there is no spin splitting in the $E_1$, $H_1$, and $H_2$ subbands for a [001] oriented cylindrical nanowire.

arXiv comment8 pages, 3 figures, published version

References in corpus (29)

• 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
• Topological Insulators with Inversion Symmetry
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Observation of Quantum Spin Hall States in InAs/GaSb Bilayers under Broken Time-Reversal Symmetry
• Band structure of semimagnetic Hg1-yMnyTe quantum wells
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Elemental Topological Insulator with a Tunable Fermi Level: Strained α-Sn on InSb(001)
• Split Dirac cones in HgTe/CdTe quantum wells due to symmetry-enforced level anticrossing at interfaces
• Engineering topological phases in the Luttinger semimetal $\alpha$-Sn
• Tensile Strained Gray Tin: a New Dirac Semimetal for Observing Negative Magnetoresistance with Shubnikov-de-Haas Oscillation
• Surface and Edge States in Topological Semi-metals
• Robust Level Coincidences in the Subband Structure of Quasi 2D Systems
• 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
• Splitting of Dirac cones in HgTe quantum wells: Effects of crystallographic orientation, interface-, bulk-, and structure-inversion asymmetry
• Subband structure of a cylindrical HgTe nanowire: transition from normal type to inverted type
• Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire
• Low-energy effective Hamiltonian and end states of an inverted HgTe nanowire