I'm reading this article about twisted TMD homobilayers (https://arxiv.org/abs/1807.03311) and there are certain topological properties that I don't understand:
On page 3, in the paragraph next to Fig 3 they said "Spin-valley locking implies that when the chemical potential is in the gap between the two topmost bands, the twisted homobilayer is not only a valley Hall insulator but also a quantum spin Hall insulator, i.e, a topological insulator". I don't get why they have this conclusion and the relation with the Chern numbers of the first, second band and the Fermi level. Up until now I only know about the TKNN Invariants which connect the Hall conductivity and the sum of bands' Chern number below the Fermi level, however a band with non-zero Chern number above the Fermi level has no physical sense to me.
Thank you in advance.