Landauer conductance in the complex domain: A path to find closed-form solutions

TL;DR

This paper introduces a novel method to evaluate the Landauer conductance by analyzing the transmission function in the complex domain, resulting in a closed-form expression that simplifies calculations for mesoscopic systems.

Contribution

The authors develop a general approach to compute the transmission function in the complex domain, revealing pole structures and deriving a closed-form solution for conductance.

Findings

Identification of complex-conjugated pole pairs responsible for transmission peaks

Derivation of a closed-form expression for the transmission function

Enhanced understanding of conductance in mesoscopic systems

Abstract

The Landauer formula allows us to describe theoretically the conductance in terms of the transmission function in a mesoscopic system. We propose a general method to evaluate the transmission function in the complex domain for systems connected to semi-infinite atomic chains. This reveals the presence of complex-conjugated pairs of simple poles that are responsible for transmission peaks in the real-domain evaluations. This leads us to formulate a closed-form expression for the transmission function.