Acoustic-phonon decoherence and electron transport in metallic nanostructures

In metallic quantum wires, electron transport at low temperatures (<10 K) is anticipated to be modified by acoustic-phonon confinement. This effect is investigated numerically through the dynamic conductance dJ/dE. The role of the energy loss through the phonons from the wire to a substrate at Ts = 0.4 K is studied in cases of both strong (supported wire) and very weak (free-standing wire) acoustic coupling to the substrate characterized by the escape time τs. The phonons are shown to remain in the 1D regime until the electron energy is about 0.8 K, much smaller than the minimum mode-separation energy. The first subband essentially contributes to dJ/dE for a large phonon escape time τs, whereas for a small one it is impossible to distinguish the different modes. Finally, it is shown that the appearance of two peaks only in dJ/dE, whatever the value of τs, results from the decoherence of phonons due to surface roughness. The case of single-walled carbon nanotubes is discussed