Optical conductivity of granular aluminum films near the Mott metal-to-insulator transition

TL;DR

This study investigates the energy gap and optical conductivity of granular aluminum films near the Mott transition, revealing a crossover from BCS to BEC-like behavior as grains decouple, with results well-described by Mattis-Bardeen theory.

Contribution

It provides experimental evidence of the evolution of the energy gap and optical properties in granular aluminum films approaching the Mott transition, highlighting a BCS-BEC crossover.

Findings

The coupling ratio $2\Delta(0)/k_{B}T_{c}$ exceeds the BCS weak coupling value.

The behavior of $\sigma_{1,s}/\sigma_{1,n}$ aligns with Mattis-Bardeen theory across high resistivities.

Evidence of a transition towards BCS-BEC crossover in high resistivity samples.

Abstract

We report measurements of the energy gap of granular aluminum films by THz spectroscopy. We find that as the grains progressively decouple, the coupling ratio $2\Delta(0)/k_{B}T_{c}$ increases above the BCS weak coupling ratio $3.53$, and reaches values consistent with an approach to BCS-BEC crossover for the high resistivity samples, expected from the short coherence length. The Mattis-Bardeen theory describes remarkably well the behavior of $\sigma_{1,s}/\sigma_{1,n}$ for all samples up to very high normal state resistivities.