Fluctuation Spectroscopy in Granular Superconductors with Application to Boron-doped Nanocrystalline Diamond

TL;DR

This paper develops a comprehensive theory of fluctuation conductivity in granular superconductors, specifically applied to boron-doped nanocrystalline diamond, revealing distinct power-law behaviors and suggesting a potential new phase-breaking mechanism.

Contribution

It provides the first detailed calculation including both intergrain and intragrain effects and compares these with experimental data, highlighting the role of phase breaking in granular superconductors.

Findings

Three distinct power-law regions identified in fluctuation conductivity.

Semi-quantitative agreement with experiments only at high phase breaking.

Evidence suggesting a novel phase-breaking mechanism in granular metals.

Abstract

We perform a detailed calculation of the various contributions to the fluctuation conductivity of a granular metal close to its superconducting transition. We find three distinct regions of power law behavior in reduced temperature, $\eta=(T-T_c)/T_c$, with crossovers at $\Gamma/T_c$ and $E_{Th}/T_c$, where $\Gamma$ is the electron tunneling rate, and $E_{Th}$ is the Thouless energy of a grain. The calculation includes both intergrain and intragrain degrees of freedom. This complete theory of the fluctuation region in granular superconductors is then compared to experimental results from boron-doped nanocrystalline diamond, using the assumption of a constant phase breaking rate, $\tau_{\phi}^{-1}$. We find a semi-quantitative agreement between the theoretical and experimental results only in the case of large phase breaking. We argue that there may be a novel phase breaking mechanism in granular metals worthy of further experimental and theoretical investigation.