Multiband superconductivity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>Si</mml:mi></mml:math> determined from studying the response to controlled disorder
Kyuil Cho, M. Kończykowski, Sunil Ghimire, M. A. Tanatar, Lin‐Lin Wang, V. G. Kogan, R. Prozorov
Abstract
The London penetration depth $\ensuremath{\lambda}(T)$ was measured in a single crystal of ${\mathrm{V}}_{3}\mathrm{Si}$. The superfluid density obtained from this measurement shows a distinct signature of two almost decoupled superconducting gaps. This alone is insufficient to distinguish between ${s}_{\ifmmode\pm\else\textpm\fi{}}$ and ${s}_{++}$ pairing states, but it can be achieved by studying the effect of controlled nonmagnetic 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 $10\phantom{\rule{0.28em}{0ex}}\mathrm{C}/{\mathrm{cm}}^{2}$ ($6.24\ifmmode\times\else\texttimes\fi{}{10}^{19}$ $\text{electrons}/{\text{cm}}^{2}$) was accumulated, for which ${T}_{c}$ changed from 16.4 K in a pristine state to 14.7 K ($9.3%$). Not only is this substantial suppression impossible for a single isotropic gap, but also it is not large enough for a sign-changing ${s}_{\ifmmode\pm\else\textpm\fi{}}$ 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 physics of iron pnictides. We analyze the results using two-gap models for both $\ensuremath{\lambda}(T)$ 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, ${\mathrm{\ensuremath{\Delta}}}_{1}(0)\ensuremath{\approx}2.53\phantom{\rule{0.28em}{0ex}}\text{meV}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}(0)\ensuremath{\approx}1.42\phantom{\rule{0.28em}{0ex}}\text{meV}$, and a very weak interband coupling in the ${\text{V}}_{3}\text{Si}$ superconductor.