Phenomenological Ginzburg-Landau theory is used to calculate the possible spontaneous vortex states that may exist at corner junctions of $d_{ x^2-y^2}+ix$-wave, (where $x=s$ or $x=d_{ xy}$) and s-wave superconductors. We study the magnetic flux and the critical current modulation with the junction orientation angle $\theta$, the magnitude of the order parameter, and the magnetic field $H$. It is seen that the critical current $I_c$ versus the magnetic flux $\Phi$ relation is symmetric / asymmetric for $x=d_{ xy}/s$ when the orientation is exactly such that the lobes of the dominant $d_{ x^2-y^2}$-wave order parameter points towards the two junctions, which are at right angles for the corner junction. The conclusion is that a measurement of the $I_c(\Phi)$ relation may distinguish which symmetry ($d_{ x^2-y^2}+is$ or $d_{ x^2-y^2}+id_{ xy}$) the order parameter has.
Categories: cond-mat.supr-con
