Anisotropic sub-band splitting mechanisms in strained HgTe: a first principles study

Mercury telluride is a canonical material for realizing topological phases, yet a full understanding of its electronic structure remains challenging due to subtle competing effects. Using first-principles calculations and $\mathbf{k}\cdot \mathbf{p}$ modelling, we study its topological phase diagram under strain. We show that linearly $k$-dependent higher-order $C_4$ strain terms are important for capturing the correct low-energy behaviour. These terms lead to a nontrivial $k$-dependence of the sub-band splitting arising from the interplay of strain and bulk inversion asymmetry. This explains the camel-back feature in the tensile regime and supports the emergence of a Weyl semimetal phase under compressive strain.