I was pondering this question after I read this review:
How do the edge modes on the interface between two domains with spin-Chern number n=1/-1 of a 2D system differ from the edge modes of the system with "n=2/0" interface? Specifically in the two cases, spin-Chern numbers differ by 2 across the interface; according to the bulk-boundary correspondence, there should be 2 edge modes of the same spin in each case. However, in Z2 classification of TI, case 1 is non-trivial in both domains (n=1 and n=-1), yet case 2 is trivial (n=2 and n=0).
I'm guessing in case 1, we do have edge modes that are against impurity and do not backscatter, but in case 2, that is not the case. Am I thinking in the right path? Is there any materials that discuss about this question?