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.

Synthetic non-Abelian gauge fields and gravitomagnetic effects in tilted Dirac cone systems

“…Furthermore, TDFs are proposed in the antiferromagnetic phase of the Iron-based superconductors as excitations above a spin density wave mean field state [22]. Angular resolved photoemission measurements of Varykhalov et al which is also supported by ab initio calculations, find a tilted Dirac cone on the metallic surface of W caused by Rashba spin-orbit interaction [23]. Ultra-low dissipation in the conductivity of BaFe 2 As 2 was attributed to the tilted Dirac cone in its spectrum [24].…”

Rashba splitting of the Tamm surface state on Re(0001) observed by spin-resolved photoemission and scanning tunneling spectroscopy

“…A Dirac-like surface state with linear dispersion and Rashba-type spin signature resides within this gap. Further experimental [15][16][17][18][19][20][21] as well as theoretical work [10,11,18,22,23] revealed the orbital d character of surface states on W(110), which is in contrast to the common orbital sp character of surface states (Shockley-type surface states) of topological insulators. In this case the surface state has been identified as a surface resonance that extends into the bulk.…”

Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones

“…In extension to the well-known case of graphene, Dirac cones can in general possess valley-dependent tilt 23 . There are only a handful of 2D electronic systems that have been predicted to host these tilted cones [24][25][26][27][28][29][30][31][32][33] , one of which is 8-Pmmn borophene 23,34 , which has attracted considerable attention. In general, boron-based nanomaterials are a growing field of interest [35][36][37] ; indeed, exploring the tilt of 2D Dirac cones in the context of 8-Pmmn borophene has recently led to a plethora of theoretical works spanning many fields of research from optics to transport, and many more.…”