On the statistical significance of the conductance quantization

TL;DR

This paper investigates the statistical origins of conductance quantization in atomic-scale metallic contacts using a simplified model and Random Matrix Theory, showing that conductance distributions become sharply peaked near quantized values as lead width increases.

Contribution

It introduces a statistical model based on Random Matrix Theory to explain conductance quantization phenomena in atomic contacts, highlighting the role of lead width.

Findings

Conductance distribution peaks near integer multiples of the quantum of conductance as lead width increases.

The model predicts a sharp conductance peak due to statistical effects, not just quantum mechanics.

Results suggest conductance quantization can have a statistical origin in atomic-scale contacts.

Abstract

Recent experiments on atomic-scale metallic contacts have shown that the quantization of the conductance appears clearly only after the average of the experimental results. Motivated by these results we have analyzed a simplified model system in which a narrow neck is randomly coupled to wide ideal leads, both in absence and presence of time reversal invariance. Based on Random Matrix Theory we study analytically the probability distribution for the conductance of such system. As the width of the leads increases the distribution for the conductance becomes sharply peaked close to an integer multiple of the quantum of conductance. Our results suggest a possible statistical origin of conductance quantization in atomic-scale metallic contacts.