I am told edge states of topological insulators are free from back scattering. Does this mean topological insulators have no resistance if only edge states are taken into account?


The edge states of a topological insulator are not superconducting, because the current is carried by ordinary electrons, not by a supercurrent of condensed Cooper pairs.

The electrons in the edge state of a topological insulator are indeed prohibited by time-reversal symmetry from scattering off a stationary impurity (elastic backscattering). On the other hand, at finite temperature they are still vulnerable to back-scattering due to the thermal vibrations of the solid or multi-particle interactions (inelastic backscattering). See, for example, the paper http://arxiv.org/abs/1303.1766. Thus, the resistivity goes to zero as the temperature approaches zero, but is never exactly zero at finite temperature.

This is contrast to superconductors, which actually do have exactly zero resistivity below the critical temperature, because the supercurrent is a collective motion, not carried by ordinary electrons, and thus is not vulnerable to any kind of backscattering (elastic or inelastic).

And of course, topological insulators do not exhibit the Meissner effect, which arguably is the defining characteristic of a superconductor.

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