Temperature dependent anisotropy of the penetration depth and coherence length in MgB$_2

TL;DR

This study measures how the anisotropies of the penetration depth and coherence length in MgB$_2$ vary with temperature, revealing opposite temperature dependencies but converging near the critical temperature, consistent with two-gap superconductor theories.

Contribution

First direct measurements of temperature-dependent anisotropies of both penetration depth and coherence length in MgB$_2$, confirming theoretical predictions for two-gap superconductors.

Findings

$ ext{γ}_ ext{λ}$ and $ ext{γ}_ ext{ξ}$ have opposite temperature dependencies.

Near $T_c$, $ ext{γ}_ ext{λ}$ and $ ext{γ}_ ext{ξ}$ converge to approximately 1.75.

Results agree with theories considering MgB$_2$ as a two-gap superconductor.

Abstract

We report measurements of the temperature dependent anisotropies ($\gamma_\lambda$ and $\gamma_\xi$) of both the London penetration depth $\lambda$ and the upper critical field of MgB$_2$. Data for $\gamma_\lambda=\lambda_c/\lambda_a$ was obtained from measurements of $\lambda_{a}$ and $\lambda_c$ on a single crystal sample using a tunnel diode oscillator technique. $\gamma_\xi=H_{c2}^{\parallel c}/H_{c2}^{\bot c}$ was deduced from field dependent specific heat measurements on the same sample. $\gamma_\lambda$ and $\gamma_\xi$ have opposite temperature dependencies, but close to $T_c$ tend to a common value ($\gamma_\lambda\simeq \gamma_\xi=1.75\pm0.05$). These results are in good agreement with theories accounting for the two gap nature of MgB$_2$