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

TL;DR

This paper develops a microscopic theory to analyze how crystallographic orientation and various asymmetries affect the splitting and structure of Dirac cones in HgTe quantum wells, revealing orientation-dependent effects.

Contribution

It introduces a detailed microscopic model that accounts for inversion asymmetries and crystallographic orientation, providing analytical expressions for the Dirac state spectrum in HgTe quantum wells.

Findings

Dirac cone degeneracy is lifted by asymmetries causing anticrossing.

Splitting of Dirac cones into Weyl cones depends on crystallographic orientation.

Analytical formulas for energy spectrum in different orientations are derived.

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.