Phase coherence and the effect of an ac electric field on the conductance of a disordered one-dimensional system

We have studied electron phase coherence in thin (i.e., small-diameter) Sb wires at low temperatures. First, we have investigated the effect of a microwave electric field ${\mathit{E}}_{\mathrm{ac}}$. This field limits the phase coherence, and thereby affects the conductance. We have also used the magnetoresistance to measure the phase-coherence length, ${\mathit{L}}_{\mathrm{\phi }}$, when ${\mathit{E}}_{\mathrm{ac}}$=0. The results for the phase-coherence time obtained from the measurements of ${\mathit{L}}_{\mathrm{\phi }}$ are in agreement with the values obtained from the microwave experiments, and both are in reasonably good agreement with the theory. Below about 4 K, phase coherence is limited by electron-electron scattering. The microwave measurements show that the electron-electron phase-coherence time is a function of the cross-sectional area of the wire. The variation with area is in qualitative, but not quantitative, agreement with the theory. Possible reasons for this discrepancy are discussed.