Emergence of flat bands and their impact on superconductivity of Mo${}_5$Si${}_{3-x}$P${}_x$

Abstract

The first-principles calculations and measurements of the magnetic penetration depths, the upper critical field, and the specific heat were performed for a family of Mo${}_5$Si${}_{3-x}$P${}_x$ superconducotrs. First-principles calculations suggest the presence of a flat band dispersion, which gradually shifts to the Fermi level as a function of phosphorus doping $x$. The flat band approaches the Fermi level at $x\simeq 1.3$, thus separating Mo${}_5$Si${}_{3-x}$P${}_x$ between the purely steep band and the steep band/flat band superconducting regimes. The emergence of flat bands lead 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 $x\lesssim 1.2$ to $\kappa \simeq 70$ for $x\gtrsim 1.4$) thus initiating the transition of Mo${}_5$Si${}_{3-x}$P${}_x$ from a moderate to an extreme type-II superconductivity.

6 pages, 4 figures