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Weyl Semimetal : TypesΒΆ

Topological Weyl semimetal (WSM) can be classified as type I in which Density of states vanishes at the Weyl nodes, and type II WSM, in which an electron pocket and a hole pocket meet at a singular point of momentum space.

From a material science perspective, the type-I Weyl semimetal can be treated as a direct negative band gap semiconductor while the type-II Weyl semimetal features an indirect negative gap

WSM_Types.png

Fig. (a) shows the type-I Weyl nodes exist at the crossing points where the conduction band (red) and valence band (blue) dip into each other. A Fermi arc (green dotted line) connects the pair of Weyl nodes. Fig.(b) shows the Fermi surface(FS) on the surface of the type-I semimetal. Fig. (c) is E-k dispersion of the type-II WSM with broken P symmetry Tilted type-II Weyl cones for at the intersection of the conduction and the valance bands. Fig. (d) shows the FS on the surface of type-II WSM. Projected bulk electron (red) and hole (blue) pockets coexist on the surface FS and touch at one discrete point, the type-II Weyl nodes.*

WSM_Types-2.png

  • A loop (dashed blue line) to show a nonzero Chern number in (a) a type-I Weyl cone and (b) a type-II Weyl cone.
  • If the Weyl point lies above the Fermi level (\(E_F\)), then for the simplest case of type-I WSM, it is clear that we can show a nonzero Chern number by counting crossings of surface states on a closed loop, which lies entirely below the \(E_F\).
  • This however is not true for the type-II WSM. If we draw a loop below \(E_F\) like before,it won't work because the loop runs into the bulk hole pocket. We can close the loop by going to \(E > E_w\), as in (e). However, then the loop must extend above \(E_F\).

References 1. Quasiparticle interference on type-I and type-II Weyl semimetal surfaces: a review 2. Fermi arc electronic structure and Chern numbers in the type-II Weyl semimetal candidate MoWTe2