Enhancement of the upper critical field in the cubic Laves-phase superconductor HfV$_{2}$ by Nb doping

We report the effect of Nb doping on the upper critical field of the cubic Laves-phase superconductor HfV$_{2}$ studied in a series of HfV$_{2-x}$Nb$_{x}$ samples with 0 $\leq$ $x$ $\leq$ 0.3 under pulsed fields up to 30 T. The undoped HfV$_{2}$ undergoes a martensitic structural transition around 110 K, and becomes superconducting below $T_{\rm c}$ = 9.4 K. Upon Nb doping, while the structural transition is suppressed for $x$ $\geq$ 0.1, a maximum in $T_{\rm c}$ of 10.1 K and zero-temperature upper critical field $B_{\rm c2}$(0) of 22.4 T is found at $x$ = 0.2, which is ascribed to an increase of the density of states at the Fermi level. For all samples, the temperature dependence of $B_{\rm c2}$ can be well described by the Werthamer-Helfand-Hohenberg (WHH) theory that takes into account both the spin paramagnetic effect and spin orbit scattering. In addition, a comparison is made between the $B_{\rm c2}$ behavior of HfV$_{2-x}$Nb$_{x}$ and those of Nb-Ti and Nb$_{3}$Sn.