A Is Graphene a Two-Dimensional Weyl Semimetal with Spin Degenerate Dirac Bands?

[Newstein]

I'm recently interested in the topological/Weyl semimetals, but I'm not an expert on the theory.
Most papers just define Weyl semimetal as a material that have pairs of Weyl points with opposite Berry curvature. Here in graphene, the Berry curvature of the Dirac cones at K and K' point is also opposite. So can we call graphene as a two-dimensional Weyl semimetal?
For the Weyl semimetal candidates in literature, SOC is important, and each Weyl point is spin polarized. The Dirac bands of graphene are spin degenerate. Is the definition of Weyl semimetal also based on the SOC?

 

[radium]

Well you should first note that the Dirac points in graphene are technically gapped once you add SOC (hence the QSHE). Weyl semimetals are more robust since the Weyl points are connected by a Fermi arc and cannot be annihilated unless you bring the two together (this could also produce a Dirac semimetal though if there is some symmetry keeping the two Weyl points pinned together on a line or a point) which does not happen with SOC. Also note that in order for the Weyl points to be separated in k space, you need to break time reversal and/or inversion.

There are some examples though of systems in 2d which have Dirac points that do not gap adding SOC which are distinct from the systems I mentioned previously.

If you look on ArXiv I think there are several recent reviews on this topic.

 

[Newstein]

Well you should first note that the Dirac points in graphene are technically gapped once you add SOC (hence the QSHE). Weyl semimetals are more robust since the Weyl points are connected by a Fermi arc and cannot be annihilated unless you bring the two together (this could also produce a Dirac semimetal though if there is some symmetry keeping the two Weyl points pinned together on a line or a point) which does not happen with SOC. Also note that in order for the Weyl points to be separated in k space, you need to break time reversal and/or inversion.

There are some examples though of systems in 2d which have Dirac points that do not gap adding SOC which are distinct from the systems I mentioned previously.

If you look on ArXiv I think there are several recent reviews on this topic.

Thank you so much!