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

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 eV to 3 eV. Our calculations quantitatively agree with the experimentally observed concentration-dependent increase of $T_c$, and its maximal value of about $20\%$.