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

TL;DR

This study combines first-principles calculations and experimental measurements to reveal how flat bands emerging in Mo$_5$Si$_{3-x}$P$_x$ superconductors significantly alter their superconducting properties, especially near a critical doping level.

Contribution

It demonstrates the impact of flat band emergence on superconducting parameters and the transition from moderate to extreme type-II superconductivity in Mo$_5$Si$_{3-x}$P$_x$.

Findings

Flat bands approach the Fermi level at x≈1.3.

Superconducting coherence length decreases sharply.

Ginzburg-Landau parameter increases from ~25 to ~70.

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.