Spontaneous surface flux pattern in chiral p-wave superconductors - revisited

In chiral $p$-wave superconductors, magnetic flux patterns may appear spontaneously when translational symmetry is broken such as at surfaces, domain walls, or impurities. However, in the candidate material Sr$_2$RuO$_4$ no direct signs of such magnetic fields have been detected experimentally. In this paper, the flux pattern at the edge of a disk-shaped sample is examined using the phenomenological Ginzburg Landau approach. The detailed shape of the flux pattern, including self-screening, is computed numerically for different surface types by systematically scanning a range of boundary conditions. Moreover, specific features of the electronic structure are included qualitatively through the coefficients in the Ginzburg Landau functional. Both the shape and the magnitude of the flux pattern are found to be highly sensitive to all considered parameters. In conclusion, such spontaneous magnetic flux patterns are not a universal feature of chiral $p$-wave superconductors.