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Imagine if you have a 2D topological insulator system where you can bring together the helical edge states from the opposite boundaries to interact (say, by a voltage gate or by a narrow constriction). Now, consider you have electron-electron interaction and your system can be described in terms of Luttinger theory.

I've read because of time-reversal symmetry (TRS), these helical states are only scattered by dispersive and forward scattering process. I can't understand how/why there are only these two possibilities to scatter if in the interaction process you destroy the TRS.

Can someone explain to me how the TRS influences the scattering process in this kind of system?

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