p-wave superconductors in magnetic fields

The possibility of vortex solutions existing for a bulk superconductor with $p$-wave pairing and isotropic normal-state properties is investigated on the basis of Gorkov's theory of weakly coupled superconductors. Assuming translational symmetry in the direction of the magnetic field only anisotropic states are found. Among these the polar state gives the highest upper critical field. States of the Anderson-Brinkman-Morel type are also found. Apart from the absence of Pauli paramagnetic limiting, the temperature dependence of the corresponding upper critical fields does not differ dramatically from that obtained for $p$-wave superconductors. Contrary to the predictions for the case of fast rotating superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, which is closely related to the problem considered here, it appears to be impossible to construct vortex lattices without singular vortex cores.