Time-reversal symmetry and Z2 topology
Time-reversal symmetry can protect helical edge modes even when total Chern number vanishes.
$$\nu\in\mathbb Z_2=\{0,1\}$$
What this means
Time-reversal symmetry can protect helical edge modes even when total Chern number vanishes.
Deep dive: mathematical and physical mechanism
For spinful electrons $\mathcal T^2=-1$ produces Kramers degeneracy at time-reversal-invariant momenta. The $\mathbb Z_2$ invariant distinguishes ordinary and quantum spin Hall insulators; it can be evaluated via sewing matrices, Wilson-loop flow, or parity eigenvalues when inversion symmetry holds.
How it appears in quantum phenomena
Quantum spin Hall materials exhibit counterpropagating spin-correlated edge states.
Assumptions, caveats and limitations
Elastic nonmagnetic backscattering is suppressed for an isolated Kramers pair, not all possible scattering or interactions.
Connect the ideas
For context, see the Topological Band Theory topic guide and the reading references.