We demonstrate that electrostatic interactions between helical electrons at the edge of a quantum spin Hall insulator and a dynamical impurity can induce quasi-elastic backscattering. Modelling the impurity as a two-level system, we show that transitions between counterpropagating Kramers-degenerate electronic states can occur without breaking time-reversal symmetry, provided that the impurity also undergoes a transition. The associated electrical resistance has a weak temperature dependence down to a non-universal temperature scale. Our results extend the range of known backscattering mechanisms in helical edge modes to include scenarios where electron tunnelling out of the system is absent.
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