In various 2D topological insulator materials (like halogenated arsenene and stanene cyanide), it is found that there is zero band gap without spin-orbit coupling (SOC) and a certain band gap with SOC. Is this a confirmation that the material is a topological insulator? Is it possible for a topologically nontrivial material to have zero band gap without SOC and a band gap with SOC? What is the physical reason for the band gap opening with SOC in 2D topological insulator materials?
https://www.nature.com/articles/srep28487
https://www.nature.com/articles/srep18604
Sabuhi Badalov
Dear Md. Mobinul Haque,
It should be noted that:
- Topological insulators comprising of a class of remarkably spin-orbital-coupled (SOC) nonmagnetic materials are insulating in bulk. Still, they have gapless edge or surface states that are topologically protected by time-reversal symmetry on the boundary.
- However, if the system is not centrosymmetric as 2D silicon or has heavy atoms as Bi and Te, SOC should cause splitting of zero bandgaps and give a small bandgap. You can see it in any similar system.
- However, you cannot refer mentioned point to topological Weyl systems. You should note that the “Dirac” point found in graphene and some ferromagnetic materials is conceptually different from the Weyl point in Topological materials. The nodal points in those systems are unstable under spin-orbit coupling, whereas the 2D Weyl point must be robust against SOC. In addition, the nodal point in graphene is fourfold degenerate if the spin is counted, whereas a 2D Weyl point is twofold degenerate.
- A Weyl point is topologically stable in bulk materials: Any perturbation can only displace it but cannot destroy it. However, in 2D, the topological protection is lost because of the reduced dimension, and additional crystal symmetries must be required for stabilizing a Weyl point. A prerequisite for realizing a topological Weyl system, whether 2D or 3D, is to break either the inversion (P) or the time-reversal (T) symmetry because otherwise, each band would be at least twofold spin degenerate, and their crossing point would be at least fourfold degenerate, not of Weyl type.
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