Surface states in HgTe and α-Sn semimetals in various topological regimes

We revisit theoretically the problem of surface states in semiconductors with inverted-band structures, such as α-Sn and HgTe. We unravel the confusion that arose over the past decade regarding the origin of the surface states, their topological nature, and the role of strain. Within simple and exactly solvable models, we reconcile different solutions found in the 1980s with the results obtained from modern-day numerical simulations.

We consider biaxial in-plane strain that is either tensile or compressive, leading to different branches of surface states for topological insulators (TIs) and Dirac semimetals (DSMs), respectively. We show that in TI regime strain is a smooth deformation to the surface states not leading to any drastic change of the physical properties in these materials, in contrast to what has recently been advanced in the literature. In DSM regime, however, strain strongly changes the surface state spectrum.

We have also investigated the surface states in HgTe material under an in-plane compressive strain and taking into account a bulk inversion asymmetry, which leads to a nodal-line-semimetal regime. Again, these results are qualitatively different from the ones previously published.

Our results can help in interpreting numerous experiments on topological surface states originating from inverted-band semiconductors.