Andreev bound states in Josephson junctions: unconventional pairing symmetries in weak magnetic field and strong-field formalism

Abstract

The supercurrent in the normal region of a superconductor - normal metal - superconductor structure (SNS), when exposed to an external magnetic field, is studied. The current is found via the energy levels of the Andreev bound states of the system. For an ordinary low-$T_c$ SNS-junction in a weak magnetic field it is found that a linear vortex pattern occurs in the current density. If the normal metal is substituted by a ferromagnet (SFS) it is found that the strength and direction of the current vortices can be controlled by the Zeeman field strength. The vortex pattern changes significantly if the low-$T_c$ superconductors in the SNS-junction are substituted by high-$T_c$ superconductors with $d$-wave pairing. Interestingly, it is found that in the presence of a subdominant $s$-wave gap in the high-$T_c$ superconductors, the symmetry of the vortex pattern is lost. Analytical expressions for the precise gap orientation producing this phenomenon are derived. Numerical simulations of the system demonstrate that the supercurrent vortex pattern can be spatially controlled via the orientation of the $d$-wave gap and via the Zeeman field, and could open new perspectives with regard to tailored quantum current distributions. A conventional SNS-junction in a strong magnetic field is also studied in which semiclassical orbits could be classified from energy levels found quantum mechanically with use of numerical calculations. It is found that if the radius of the Lorentz cyclotron is small enough the energy levels will not contribute to the Josephson current.