Exact analytic formula for conductance predicting a tunable Sommerfeld-Arrhenius thermal transition within a single-step tunneling mechanism in molecular junctions subject to mechanical stretching

TL;DR

This paper derives an exact analytic formula for conductance in molecular junctions, revealing a tunable thermal transition from Sommerfeld to Arrhenius behavior, observable in experiments and adjustable by mechanical stretching.

Contribution

It provides the first exact closed-form expression for conductance in single-level tunneling models at any temperature, elucidating a tunable thermal transition mechanism.

Findings

Exact conductance formula valid at all temperatures.

Identification of a continuous transition from Sommerfeld to Arrhenius regimes.

Prediction of observable, tunable thermal transition in real molecular junctions.

Abstract

We show that the conductance $G$ of molecular tunnel junctions wherein the charge transport is dominated by a single energy level can be expressed in closed analytic form which is exact and valid at arbitrary temperature $T$ and model parameter values. On this basis, we show that the single-step tunneling mechanism is compatible with a continuous thermal transition from a weakly $T$-dependent $G$ at low $T$ (Sommerfeld regime) to a nearly exponential $1/T$-dependent $G$ at high $T$ (Arrhenius-like regime). We predict that this Sommerfeld-Arrhenius transition can be observed in real molecular junctions % (e.g., based on perylene diimide) and can be continuously tuned, e.g., via mechanical stretching.