Abstract
We have calculated the structure of an isolated vortex line near ${H}_{c1}$ 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 \ensuremath{\nu} $(\ensuremath{\nu}=5/13$ for a square) we obtain an additional uniaxial vortex of opposite phase \ensuremath{\varphi} within the core region. This yields a small correction of the current density ${j}_{\ensuremath{\varphi}}$ and the magnetic field, which are proportional to $\mathrm{cos}(4\ensuremath{\varphi}).$ For a nodal f-wave ABM state that is more consistent with recent experiments we obtain analogous results with an effective $\ensuremath{\nu}=1/2$ for a circular Fermi surface.
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