Transport through a multiply connected interacting meso-system using the Keldysh formalism

TL;DR

This paper develops a simplified current formula for interacting mesoscopic systems using the Keldysh formalism, revealing interference effects and temperature-independent conductance points in a triangular interferometer.

Contribution

It introduces an exact current formula applicable to systems with many sites and interactions, especially under left-right symmetry, simplifying calculations in mesoscopic transport.

Findings

Interference effects lead to temperature-independent conductance points.

The derived formula is exact under left-right symmetry, avoiding the lesser Green function.

Comparison shows the new formula outperforms Ng's ansatz in accuracy.

Abstract

We apply the Keldysh formalism in order to derive a current formula easy to use for a system with many sites, one of which is interacting. The main technical challenge is to deal with the lesser Green function. It turns out that, in the case of the left-right symmetry, the knowledge of the lesser Green function is not necessary and an exact current formula can be expressed in terms of retarded Green functions only. The application is done for a triangular interferometer which gives a good account of the Fano-Kondo effect. It is found that the interference effects, in the context of Kondo correlations, give rise to a point in the parameters space where the conductance is temperature-independent. We include a comparison with the results from the Ng's ansatz, which are less accurate, but can be used also in the absence of the above mentioned symmetry.