# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1901.02814