  Niobium-zirconium (Nb-Zr) alloy is an old superconductor that is a promising
new candidate for superconducting radio-frequency (SRF) cavity applications.
Using density-functional and Eliashberg theories, we show that addition of Zr
to a Nb surface in small concentrations increases the critical temperature
$T_c$ and improves other superconducting properties. Furthermore, we calculate
$T_c$ for Nb-Zr alloys across a broad range of Zr concentrations, showing good
agreement with the literature for disordered alloys as well as the potential
for significantly higher $T_c$ in ordered alloys near 75%Nb/25%Zr composition.
We provide experimental verification on Nb-Zr alloy samples and SRF sample test
cavities prepared with either physical vapor or our novel electrochemical
deposition recipes. These samples have the highest measured $T_c$ of any Nb-Zr
superconductor to date and indicate a reduction in BCS resistance compared to
the conventional Nb reference sample; they represent the first steps along a
new pathway to greatly enhanced SRF performance. Finally, we use
Ginzburg-Landau theory to show that the addition of Zr to a Nb surface
increases the superheating field $B_{sh}$, a key figure of merit for SRF which
determines the maximum accelerating gradient at which cavities can operate.
