Strain tuning of Dirac states at the SnTe (001) surface

Abstract

The topological crystalline insulator SnTe belongs to the recently discovered class of materials in which a crystalline symmetry ensures the existence of topologically protected surface states. The bulk band structure of SnTe is characterized by a band inversion at the four equivalent $L$ points, giving rise to a mirror Chern number of ${n}_{\mathcal{M}}=\ensuremath{-}2$. The (001) surface exhibits four Dirac cones which lie at non-time-reversal-invariant points close to $\overline{X}$ and $\overline{Y}$ and are protected by the $(\overline{1}10)$ and (110) mirror symmetries. In contrast to topological insulators, this symmetry can be broken via deformations of the crystal. This opens up new possibilities for manipulating the Dirac states and inducing a controllable gap. Here, we have employed density-functional theory to investigate the response of the Dirac states to applied distortions from first principles. Our calculations show that a local gap of up to $\ensuremath{\approx}30\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ can be introduced via lattice deformations that break at least one of the underlying mirror symmetries. It is formed at either all four or just two cones, depending on the direction of the displacement vector, making it possible to create either a global gap or a state where opened and intact Dirac cones coexist. Notably, applying these deformations at the surface only can already induce the gap. If the complete slab is distorted, bulk bands are pushed into the gap making the whole system metallic.