Structure of a single vortex for a hypothetical p-wave and f-wave superconducting state in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

We have calculated the structure of an isolated vortex line near $H_{c1\mathrm{}}$ on the basis of the Ginzburg-Landau functional for planar Anderson-Brinkman-Morel (ABM) superconducting states of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4.$ For a nodeless p-wave ABM state and a circular Fermi surface we find the same solution as for s-wave pairing. For tetragonal deformation of the Fermi surface with anisotropy parameter ν $(\nu =5/13\mathrm{}$ for a square) we obtain an additional uniaxial vortex of opposite phase φ within the core region. This yields a small correction of the current density $j_{\phi }$ and the magnetic field, which are proportional to $\cos \left(4\mathrm{}\phi \right).\mathrm{}$ For a nodal f-wave ABM state that is more consistent with recent experiments we obtain analogous results with an effective $\nu =1/2\mathrm{}$ for a circular Fermi surface.