An interesting feature of the topological insulators is that even though the bulk is insulating it is guaranteed that there is a metallic boundary state, which is called a topological surface/edge state. There are various topological phases depending on symmetries that protect the topological invariant of the system. For example, for quantum spin Hall effect, the stability of the topological invariant (called spin Chern number or Z2 invariant) and thus the boundary state are protected by the time-reversal symmetry. For this reason, even though the topological boundary state is stable against nonmagnetic impurities, magnetic impurities can destroy the topological boundary state by opening the gap as it breaks the time-reversal symmetry. Anyway, the topological boundary state shows unique transport effects due to its dissipationless nature. This leads to quantized conductance, which can be measured in the nonlocal transport geometry. Intuitively, it is a kind of one-way street for electrons.

Recent papers by Canonico *et al.* [PRB 101, 075429 (2020); PRB 101, 161409(R) (2020)] proposed an idea of orbital Hall insulator. And they found specific material examples: transition metal dichalcogenides. The authors observed that the orbital Hall conductivity is finite even in insulating systems. After reading these papers, I have been curious about existence of the boundary state and a topological invariant that is closely reltaed to the orbital angular momentum. But it wasn’t long before the authors answer to these questions.

In a paper published on arXiv in this month, Cysne *et al.* have shown that transition metal dichalcogenides are not just insulators. They are “orbital Chern insulators”, which is quite analogous to spin Chern insulator/quantum spin Hall insulator. They proposed the concept of orbital Chern number, a topological invariant that characterizes orbital Hall insulating phase. And by explicit calculation of the zigzag nanoribbon geometry, they have shown that nonzero orbital Chern number has direct consequence on the boundary state.

The finding of this new phase of matter has lots of implications on orbital transport. I find that it would be very interesting to come up with a way to utilize the orbital Hall current in this system. Especially, since the boundary state is dissipationless by its chiral nature, it may be used as a resistenceless channel for the orbital transport. This goes a way beyond what people normally expect: Orbital information dephases quicly due to crystal field splitting.

For those who are interested, here is a link of the paper:

* Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides, *Tarik P. Cysne, Marcio Costa, Luis M. Canonico, M. Buongiorno Nardelli, R. B. Muniz, Tatiana G. Rappoport, arXiv:2020.07894