Weak inter-band coupling in Mg$^{10}$B$_{2}$: a specific heat analysis

TL;DR

This study uses specific heat measurements to analyze the superconducting state of Mg$^{10}$B$_{2}$, revealing weak inter-band coupling and a very small superconducting gap in one sample, confirming theoretical predictions.

Contribution

It provides a detailed specific heat analysis of Mg$^{10}$B$_{2}$, demonstrating weak inter-band coupling through a modified analysis method and confirming theoretical models.

Findings

Weak inter-band coupling confirmed by deviation function analysis

Observation of a low superconducting gap in one sample

Modified entropy conservation approach for band-specific analysis

Abstract

The superconducting state of Mg$^{10}$B$_{2}$ is investigated by specific heat measurements in detail. The specific heat in the normal state is analyzed using a recently developed computer code. This allows for an extraction of the electronic specific heat in the superconducting state with high accuracy and a fair determination of the main lattice features. One of the two investigated samples shows a hump in the specific heat at low temperatures within the superconducting state, accompanied by an unusual low value of the small gap, $\Delta_{\pi}(0)=1.32 meV$, pointing to a very weak inter-band coupling. This sample allows for a detailed analysis of the contribution from the $\pi$-band to the electronic specific heat in the superconducting state. Therefore the usual analysis method is modified, to include the individual conservation of entropy of both bands. From analyzing the deviation function $D(t)$ of MgB$_{2}$, the theoretically predicted weak inter-band coupling scenario is confirmed.