Local non-equilibrium distribution of charge carriers in a phase-coherent conductor

TL;DR

This paper develops a theoretical framework using the scattering matrix approach to describe local non-equilibrium charge distributions in phase-coherent conductors, linking conductance measurements to local densities of states and quantum coherence effects.

Contribution

It introduces generalized Bardeen-like formulas connecting conductance to local densities of states and derives a non-equilibrium distribution function incorporating quantum coherence.

Findings

Conductance is proportional to local partial densities of states.

The local non-equilibrium distribution function reflects quantum phase coherence.

Results are demonstrated for ballistic and diffusive conductors.

Abstract

We use the scattering matrix approach to derive generalized Bardeen-like formulae for the conductances between the contacts of a phase-coherent multiprobe conductor and a tunneling tip which probes its surface. These conductances are proportional to local partial densities of states, called injectivities and emissivities. The current and the current fluctuations measured at the tip are related to an effective local non-equilibrium distribution function. This distribution function contains the quantum-mechanical phase-coherence of the charge carriers in the conductor and is given as products of injectivities and the Fermi distribution functions in the electron reservoirs. The results are illustrated for measurements on ballistic conductors with barriers and for diffusive conductors.