Emergence of flat bands and their impact on superconductivity in Mo5Si3-xPx

Abstract

The superconductivity in systems containing the dispersionless (flat) bands might appear to be paradoxical, since the conventional Bardeen–Cooper–Schrieffer theory requires an infinite enhancement of the carrier masses. At the same time, the combination of a flat and steep (dispersive) bands within the multiple band scenario are expected to enhance the superconducting response and may potentially explain a high-temperature superconductivity in cuprates and metal hydrides. Here, we report on the magnetic penetration depths, the upper critical field, and the specific heat measurements together with the first-principles calculations for Mo$_5$Si$_{3-x}$P$_x$ superconducting family. The calculated band structure features a flat band, which gradually approaches the Fermi level as a function of phosphorus doping $x$. The flat band reaches the Fermi level at $x\simeq 1.3$, leading to an abrupt change of nearly all the superconducting quantities. In particular, a strong reduction of the coherence length $\xi$ and enhancement of the penetration depth $\lambda$ result in nearly factor of three increase of the Ginzburg-Landau parameter $\kappa=\lambda/\xi$ (from $\kappa\simeq 25$ for $x< 1.3$ to $\kappa\simeq 70$ for $x> 1.3$) thus initiating the transition of Mo$_5$Si$_{3-x}$P$_x$ from a moderate to an extreme type-II superconductivity. The superfluid density data placed on the 'Uemura plot' result in two separated branches thus indicating that emergency of a flat band leads to enhancement of correlations between conducting electrons.