Splitting of Dirac cones in HgTe quantum wells: Effects of crystallographic orientation, interface-, bulk-, and structure-inversion asymmetry

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