Upper critical field of $p$-wave superconductors with orthorhombic symmetry

Recent experiments on exotic ferromagnetic superconducting materials such as UCoGe and topological superconductors such as Cu$_{x}$Bi$_{2}$Se$_{3}$, have spawned renewed interest in $p$-wave superconductivity. We present an extension of the Scharnberg-Klemm theory of $H_{c2}$ in $p$-wave superconductors to cases of partially broken symmetry in an orthorhombic crystal. Using a uniaxial anisotropic pairing interaction as is appropriate for the low-field regime of UCoGe, we have shown that a field induced crossover from one $p$-wave state to another can lead to kinks in $H_{c2}(T)$, which can mimic upward curvature in all three crystal axis directions. Reasonably good fits to the low-field UCoGe data are obtained. We have also investigated the angular dependence of the axial $p$-wave state, which might prove useful in identifying the $p$-wave state present in certain materials, and possibly suggest new experiments on well known $p$-wave superconductors.