Upper Critical Field inp-Wave Superconductors with Broken Symmetry

A uniaxially anisotropic $p$-wave interaction is shown to lead to either a polar or an axial state. We calculate the anisotropy of $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ with the assumption that $E_{\mathrm{F}}\gg k_{\mathrm{B}}{T}_c$. Weak-interaction anisotropy leads to a kink in $H_{c2,\perp }\mathrm{}\left(T\right)\mathrm{}$. Otherwise, our results are qualitatively similar to those for an anisotropic $s$-wave material. Our results indicate that the anisotropy of the $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ data obtained for U${\mathrm{Pt}}_3$ cannot be explained as intrinsic for a $p$-wave superconductor unless $E_{\mathrm{F}}\cong k_{\mathrm{B}}{T}_c$.