Conductance of nanosystems with interaction

TL;DR

This paper develops a formalism to calculate the conductance of interacting nanosystems at zero temperature using ground-state energies of an auxiliary ring system, applicable when the ground state is a Fermi liquid.

Contribution

It introduces an exact method linking conductance to ground-state energy in Fermi liquid systems, applicable to complex mesoscopic structures.

Findings

The formalism is exact for Fermi liquid ground states.

Conductance can be derived from the flux dependence of ground-state energy.

Application demonstrated on quantum dot and Aharonov-Bohm ring with Kondo physics.

Abstract

The zero-temperature linear response conductance through an interacting mesoscopic region attached to noninteracting leads is investigated. We present a set of formulas expressing the conductance in terms of the ground-state energy of an auxiliary system, namely a ring threaded by a magnetic flux and containing the correlated electron region. We prove that the formalism is exact if the ground state of the system is a Fermi liquid. We show that in such systems the ground-state energy is a universal function of the magnetic flux, where the conductance is the relevant parameter. The method is illustrated with results for the transport through an interacting quantum dot and a simple Aharonov-Bohm ring with Kondo-Fano resonance physics.