Tilted Dirac cone on W(110) protected by mirror symmetry

Abstract

Topologically nontrivial states reveal themselves in strongly spin-orbit coupled systems by Dirac cones. However, their appearance is not a sufficient criterion for a topological phase. In topological insulators, where these states protect surface metallicity, they are straightforwardly assigned based on bulk-boundary correspondence. On metals, where these states are suspected to have tremendous impact as well, e.g., in catalysis, their topological protection is difficult to assess due to the lacking band gap and the frequent assignment to topological properties appears unjustified. Here, we discover by angle-resolved photoemission a state with the dispersion of a Dirac cone at a low-symmetry point of W(110). Our ab initio calculations predict this feature with a linear band crossing and high spin polarization. However, instead of being born by topology, the states arise from Rashba split bands and do not fundamentally depend on the opening of a spin-orbit gap. On the other hand, we find that the [001] mirror plane protects the band crossing point and renormalizes the dispersion towards a Dirac-cone shape. In this sense, the discovered state is the metal counterpart of the surface state of a topological crystalline insulator. The Dirac cone is tilted due to its origin in an accidental band crossing away from high symmetry points. Tilted Dirac cones have recently been predicted for two- and three-dimensional materials and were observed in three-dimensional Weyl semimetals. Accordingly, the protection and renormalization by mirror symmetry uncovered here are a potentially much wider spread phenomenon which does not require topological properties. Our results also indicate why the massive gapless crossing predicted for topological crystalline insulators has never been observed.