Local densities, distribution functions, and wave function correlations for spatially resolved shot noise at nanocontacts

TL;DR

This paper develops a quantum-mechanical framework to analyze local densities, distribution functions, and wave function correlations in phase-coherent multi-probe conductors, revealing how these influence shot noise and current correlations at nanocontacts.

Contribution

It introduces an exact quantum approach linking local non-equilibrium distributions to wave function correlations, including phase effects, in multi-probe nanocontacts.

Findings

Current fluctuations are determined by local non-equilibrium distribution functions.

Zero-temperature current correlations depend on spatially non-diagonal injectivities and emissivities.

Aharonov-Bohm oscillations affect shot noise correlations in conductors without flux-sensitive conductance.

Abstract

We consider a current-carrying, phase-coherent multi-probe conductor to which a small tunneling contact is attached. We treat the conductor and the tunneling contact as a phase-coherent entity and use a Green's function formulation of the scattering approach. We show that the average current and the current fluctuations at the tunneling contact are determined by an effective local non-equilibrium distribution function. This function characterizes the distribution of charge-carriers (or quasi-particles) inside the conductor. It is an exact quantum-mechanical expression and contains the phase-coherence of the particles via local partial densities of states, called injectivities. The distribution function is analyzed for different systems in the zero-temperature limit as well as at finite temperature. Furthermore, we investigate in detail the correlations of the currents measured at two different contacts of a four-probe sample, where two of the probes are only weakly coupled contacts. In particular, we show that the correlations of the currents are at zero-temperature given by spatially non-diagonal injectivities and emissivities. These non-diagonal densities are sensitive to correlations of wave functions and the phase of the wave functions. We consider ballistic conductors and metallic diffusive conductors. We also analyze the Aharonov-Bohm oscillations in the shot noise correlations of a conductor which in the absence of the nano-contacts exhibits no flux-sensitivity in the conductance.