Band inversion transition in HgTe nanowire grown along the 001 direction

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 E₁ and H₁ subbands into an anticrossing at kₙR\!=\!0, the gap-closing-and-reopening transition in the subband structure can still occur at finite wave vectors kₙR\!\!0. 24 for critical nanowire radius R\!\!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 E₁, H₁, and H₂ subbands for a 001 oriented cylindrical nanowire.