Unusual temperature dependent resistivity of a semiconductor quantum wire

We calculate the electronic resistivity of a GaAs-based semiconductor quantum wire in the presence of acoustic phonon scattering. We find that the usual Drude-Boltzmann transport theory leads to a low temperature activated behavior instead of the well-known Bloch-Gr\"uneisen power law. Many-body electron-phonon renormalization, which is entirely negligible in higher dimensional systems, has a dramatic effect on the low temperature quantum wire transport properties as it qualitatively modifies the temperature dependence of the resistivity from the exponentially activated behavior to an approximate power law behavior at sufficiently low temperatures.