Validity of the Wiedemann-Franz law in small molecular wires

TL;DR

This study investigates the finite-size effects on the Lorenz number in molecular wires, revealing different validity regimes of the Wiedemann-Franz law depending on wire length and tunneling processes.

Contribution

It demonstrates that the Wiedemann-Franz law holds only in certain regimes for small systems and compares Landauer-Büttiker and Kubo formalisms to explain discrepancies.

Findings

Wiedemann-Franz law valid in cotunneling regime for long wires

In small wires, only cotunneling regime persists

Lorenz number distribution varies with tunneling order and temperature

Abstract

We report our investigations on the finite-size effects of the Lorenz number in a molecular wire. Using Landauer-B\"uttiker formalism, we find that for sufficiently long wires there are two validity regimes of the Wiedemann-Franz (WF) law, the cotunneling and the sequential tunneling regimes, while in small systems only the first regime survives. We compare our results with the standard Kubo formalism and explain its failure to detect the WF law in small systems. Furthermore, our studies on exponentially localized disordered wires show that the Lorenz number value L_0 predicted by the WF law is obtained only in the cotunneling regime. Also, the Lorenz number L exhibits a typical distribution at different temperatures corresponding to different tunneling process. In particular, first-order tunneling results in a low value of L whereas second-order tunneling recovers the universal value L_0.