Transfer-matrix approach to the problem of electrical conduction through a series of absorbers

TL;DR

This paper presents a transfer-matrix method to analyze incoherent electrical conduction through molecular wires modeled as chains of absorbers, deriving an analytic transmission expression and showing exponential current decay with wire length.

Contribution

It introduces an analytic transfer-matrix approach for incoherent transport in molecular wires with absorbers, incorporating phase-breaking effects via imaginary potentials.

Findings

Transmission is analytically derived for finite chains.

Electrical current decays exponentially with wire length.

The method effectively models phase-breaking processes in molecular conduction.

Abstract

Here we study incoherent transport through molecular wire treated as a linear chain of absorbers, where the phase-breaking processes are modeled by the use of imaginary point-like potentials. The calculations are performed within a transfer-matrix method of the scattering theory. An analytic expression for the transmission of a finite chain in obtained, while the electrical current is then computed with the help of the Tsu-Esaki formula. In particular, it is shown that the maximal current dependence on the wire length is exponential.