Superconducting transition temperatures of pure vanadium and vanadium-titanium alloys in the presence of dynamical electronic correlations

Abstract

Ordinary superconductors are widely assumed insensitive to small concentrations of random nonmagnetic impurities, whereas strong disorder suppresses superconductivity, ultimately leading to a superconductor-insulator transition. In between these limiting cases, a most fascinating regime may emerge where disorder enhances superconductivity. This effect is discussed here for the $\beta$-phase of vanadium-titanium alloys. Disorder is modeled using the coherent potential approximation while local electronic interactions are treated using dynamical mean-field theory. The McMillan formula is employed to estimate the superconducting transition temperature, showing a maximum at a Ti concentration of around $0.33$ for a local Coulomb interaction $U$ in the range of $2$ to $3$ eV. Our calculations quantitatively agree with the experimentally observed concentration dependent increase of $T_c$, and its maximal value of about $20\%$.