Chemical potential oscillations near a barrier in the presence of transport

The electrochemical potential drop across a single scatterer in an otherwise perfect conductor measured by weakly coupled probes is investigated. Phase sensitive probes yield a spatially oscillating voltage over distances of a phase-randomization length away from a scatterer. In a single-channel conductor these oscillations have a period ${\lambda }_F$/2 similar to the Friedel oscillations. The amplitude of the oscillations is the same on either side of the scatterer. The potential drop across the obstacle also oscillates and is in general not positive. Averaging the chemical potential over these oscillations yields a potential drop which is positive but smaller than the potential drop predicted by neglecting these oscillations altogether. In a multichannel system the chemical potential fluctuations are more complex with oscillatory components of much longer period than ${\lambda }_F$. .AE