Multi-band $s_{++}$ superconductivity in $\textrm{V}_{3}\textrm{Si}$ determined from the response to a controlled disorder

TL;DR

This study investigates the multi-band $s_{++}$ superconductivity in V$_{3}$Si by measuring the London penetration depth and the effect of controlled disorder, providing evidence for two-gap $s_{++}$ pairing with weak inter-band coupling.

Contribution

The paper demonstrates that V$_{3}$Si exhibits two-gap $s_{++}$ superconductivity supported by experimental measurements and theoretical modeling, distinguishing it from $s_{ ext{pm}}$ pairing states.

Findings

Superfluid density indicates two nearly decoupled superconducting gaps.

Controlled disorder suppresses $T_c$ but not enough for $s_{pm}$ pairing.

Band structure supports two effective gaps similar to iron pnictides.

Abstract

The London penetration depth, $\lambda(T)$, was measured in a single crystal V$_{3}$Si. The superfluid density obtained from this measurement shows a distinct signature of two almost decoupled superconducting gaps. This alone is insufficient to distinguish between $s_{\pm}$ and $s_{++}$ pairing states, but it can be achieved by studying the effect of a controlled non-magnetic disorder on the superconducting transition temperature, $T_{c}$. For this purpose, the same $\text{V}_{3}\text{Si}$ crystal was sequentially irradiated by 2.5 MeV electrons three times, repeating the measurement between the irradiation runs. A total dose of 10 C/cm$^{2}$ ($6.24\times10^{19}$ electrons/$\textrm{cm}^{2}$) was accumulated, for which $T_{c}$ has changed from 16.4 K in a pristine state to 14.7 K (9.3 $\%$). This substantial suppression is impossible for a single isotropic gap, but also it is not large enough for a sign-changing $s_{\pm}$ pairing state. Our electronic band-structure calculations show how five bands crossing the Fermi energy can be naturally grouped to support two effective gaps, not dissimilar from the iron pnictides physics. We analyze the results using two-gap models for both, $\lambda(T)$ and $T_{c}$, which describe the data very well. Thus, the experimental results and theoretical analysis provide strong support for an $s_{++}$ superconductivity with two unequal gaps, $\Delta_{1}\left(0\right)\approx2.53\;\textrm{meV}$ and $\Delta_{2}\left(0\right)\approx1.42\;\textrm{meV}$, and a very weak inter-band coupling in $\text{V}_{3}\text{Si}$ superconductor.