Topological Insulator: 100% Spin Polarization & Transport Properties

[fk08]

Why is it so important to claim that the topologically protected surface states are 100% spin polarized. Is there any connection between the degree of polarization and for instance transport properties, like the absent backscattering of these states at impurities?

 

[OhYoungLions]

As far as I understand things, there is a deep connection. The point is, backscattering at impurities implies there is a valid state for the quasiparticles at the surface to scatter into, and that the potential of the impurity, written in second quantized notation, actually connects the two states.

In the case of topological insulators, states with crystal momentum k at the surface have opposite spins to states with momentum -k. What the means is that if your impurity potential can't connect states with different spin, then there is no valid state for the quasiparticles to scatter into. This is true so long as the impurity doesn't break time reversal symmetry (is nonmagnetic).

To summarize: A particle with a certain spin can't scatter off a nonmagnetic impurity into a state with opposite spin. If that's the only kind of state available, there is no scattering.