Low-energy effective Hamiltonian and end states of an inverted HgTe nanowire

Abstract

The band inversion transition in a cylindrical HgTe nanowire is inducible via varying the nanowire radius. Here we derive the low-energy effective Hamiltonian describing the band structure of the HgTe nanowire close to the fundamental band gap. Because both the $E_1$ and $H_1$ subbands have quadratic dependence on $k_z$ when the gap closes, we need to consider at least three subbands, i.e., the $E_1$, $H_1$, and $H_2$ subbands, in building the effective Hamiltonian. The resulting effective Hamiltonian is block diagonal and each block is a $3\times 3$ matrix. End states are found in the inverted regime when we solve the effective Hamiltonian with open boundary condition.

6 pages, 4 figure, published version

References in corpus (13)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Spin-orbit insulating phase in SnTe cubic nanowires: consequences on the topological surface states
• 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
• 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

Cited by in corpus (1)

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