S-Matrix Formulation of Mesoscopic Systems and Evanescent Modes

TL;DR

This paper revisits the S-matrix formulation of mesoscopic systems, highlighting the need to reinterpret the Landauer-Butikker formalism in quasi-one-dimensional systems due to evanescent modes.

Contribution

It demonstrates that the existing S-matrix formalism requires reinterpretation in quasi-one-dimensional systems because of evanescent modes, extending previous understanding.

Findings

The formalism is valid for simple 1D systems.

Evanescent modes affect the interpretation in quasi-1D systems.

Reinterpretation is necessary for accurate thermodynamic analysis.

Abstract

The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.