Enhanced Surface Superconductivity of Niobium by Zirconium Doping

Superconducting radio-frequency (SRF) cavities currently rely on niobium (Nb), and could benefit from a higher-$T_c$ surface, which would enable a higher operating temperature, lower surface resistance, and higher maximum fields. Surface zirconium (Zr) doping is one option for improvement, which has not previously been explored, likely because bulk alloy experiments showed only mild $T_c$ enhancements of 1–2 K relative to Nb. Our ab initio results reveal a more nuanced picture: an ideal bcc Nb-Zr alloy would have $T_c$ over twice that of niobium, but displacements of atoms away from the high-symmetry bcc positions due to the Jahn-Teller-Peierls effect almost completely eliminates this enhancement in typical disordered alloy structures. Ordered Nb-Zr alloy structures, in contrast, are able to avoid these atomic displacements and achieve higher calculated $T_c$ up to a theoretical limit of 17.7 K. Encouraged by this, we tested two deposition methods: a physical-vapor Zr deposition method, which produced Nb-Zr surfaces with $T_c$ values of 13.5 K, and an electrochemical deposition method, which produced surfaces with a possible 16-K $T_c$. An rf test of the highest-$T_c$ surface showed a mild reduction in BCS surface resistance relative to Nb, demonstrating the potential value of this material for RF devices. Finally, our Ginzburg-Landau theory calculations show that realistic surface doping profiles should be able to reach the maximum rf fields necessary for next-generation applications, such as the ground-breaking LCLS-II accelerator. Considering the advantages of Nb-Zr compared to other candidate materials such as ${\mathrm{Nb}}_3\mathrm{Sn}$ and Nb-Ti-N, including a simple phase diagram with relatively little sensitivity to composition, and a stable, insulating ${\mathrm{Zr}\mathrm{O}}_2$ native oxide, we conclude that Nb-Zr alloy is an excellent candidate for next-generation, high-quality-factor superconducting rf devices.

Figure 1

(a) DOS at the Fermi level using the VCA and supercell methods. The upper plot is at 12.5 at%Zr and the lower plot is at 25 at%Zr concentration. (b) Superconducting gap as a function of temperature. (c) Calculated phonon dispersion and (d) ${\alpha }^{2}F$ of Nb-Zr alloys. The blue, orange, and green lines are for pure Nb, 10 at%Zr and 20 at%Zr, respectively. As Zr concentration increases, phonons at lower frequency couple strongly with electrons, increasing the electron-phonon coupling constant.

Figure 2

Alloy $T_c$ versus composition for experiment (black, Ref. [24]), VCA (yellow squares), random supercell theory (blue circles), and Jahn-Teller-Peierls stability limit (red).

Figure 3

Electronic DOS for 50/50 Nb-Zr (a) and Nb-Mo (b) random alloys before atomic relaxation (red) and after atomic relaxation (black). (c) Histogram of atomic displacements in 50/50 Nb-Zr (red) and Nb-Mo (blue) alloys. (d) DOS curves for three different ordered 50/50 Nb-Zr alloys before (red) and after (black) applying electronic state energy broadening to reduce $N(0)$ and stabilize the structure.

Figure 4

Zr concentration $n$ versus depth $x$ for Nb-Zr samples prepared with various initial $\mathrm{Zr}$ film thicknesses and annealing conditions. Also shown is an example profile $n(x)$ [Eq. (4)], which roughly approximates one of the measured samples. We predict that an SRF cavity with this type of Nb-Zr profile on its surface could have $B_{\mathrm{sh}}\approx$ 275 mT (see Fig. 6).

Figure 5

Structural and superconducting properties of Nb-Zr samples. (a) X-ray diffraction pattern for evaporation-based samples annealed at ${600}^{\circ }\mathrm{C}$ for 10 h and subsequently etched with HF. (b) Comparison of BCS surface resistance before and after Nb-Zr alloying.

Figure 6

Calculated $B_{\mathrm{sh}}$ at $T=0$ of Nb-Zr surface layers with varying compositions [see Eq. (4)], rescaled consistent with Table 1.