Splitting of Dirac Cones in HgTe Quantum Wells: Effects of Crystallographic Orientation, Interface-, Bulk-, and Structure-Inversion Asymmetry

We develop a microscopic theory of the fine structure Dirac states in $(0lh)$-grown HgTe/CdHgTe quantum wells (QWs), where $l$ and $h$ are Miller indices. It is shown that bulk, interface, inversion asymmetry causes anticrossing levels even at zero in-plane wave vector lifts state degeneracy. In QWs critical thickness, two-fold degenerate cone gets split into non-degenerate Weyl cones. The splitting point positions dramatically depend on QW crystallographic orientation. calculate parameters related to derive effective Hamiltonian states. Further, we obtain an analytical expression for energy spectrum discuss (001)-, (013)- (011)-grown QWs.