Bulk upper critical field of clean type-II superconductors: V and Nb

The bulk upper critical field $H_{c2}$ of single crystals of Nb and V has been measured for various crystallographic orientations within the temperature range between the respective critical temperature and T≈0.06 °K. The normalized critical field averaged over all crystallographic directions $〈h\left(t\right)〉=\frac{〈H_{c2}\left(t\right)〉}{{(-\frac{d{H}_{c2}}{dt})}_{t=1}}$, where $t=\frac{T}{T_c}$, and the relative anisotropy of $H_{c2}$ for the two metals are found to be similar. The measurements support predictions of the Hohenberg-Werthamer calculation that attributes the observed anisotropy of $H_{c2}$ to the effects of an anisotropic Fermi surface. Some differences in the behavior of $H_{c2}\left(t\right)$ for the present samples can be understood qualitatively to arise from the effects of a shorter electron-collision time τ for the less pure V specimen. At very low temperatures, $H_{c2}\left(0\right)-H_{c2}\left(t\right)$ for V does not follow a t²ln(t) temperature dependence, previously observed for Nb, but can be characterized by an empirical formula t²ln(t+α) in which the constant α is conjectured to be inversely proportional to τ.