[Physics] How does time reversal symmetry work in topological insulator

Question

I am doing microelectronic devices with topological insulators. Can some one explain time reversal symmetry in a topological insulator to electrical engineering student like me?

Answer 1

I assume you refer to something like a BHZ-$\mathbb{Z}_2$-insulator (with the experimental realization of a 2d-$\text{HgTe}$-quantum well).

This model can be understood as two Chern insulators. Chern insulators have a chiral edge mode (that is, an edge mode, that propagates only in one turning sense, thus breaking time reversal). This is analogous to the way a magnetic field breaks time reversal.

The two spin channels of the BHZ model are time reversal conjugates for the spinless Chern insulator, furthermore the spin channels are flipped when applying time reversal, leading to a time reversal invariant spinful model.

I hope, I was not too technical and sufficiently detailed.