Ginzburg-Landau theory and vortex structure for ad+s-wave superconductor with orthorhombic distortion

Abstract

We study microscopically the Ginzburg-Landau (GL) theory of a $d+s$-wave superconductor with orthorhombic symmetry. The anisotropic pairing interaction due to the orthorhombic distortion leads to a second-order coupling between the $s$- and $d$-wave components which is proportional to the anisotropy parameter. This coupling induces a nonvanishing $s$-wave component even in a uniform system and a relative zero phase between the $s$- and $d$-wave components is favored. The ratio of the homogeneous bulk value of the $s$-wave component to that of the $d$-wave component decreases linearly as the temperature decreases in the vicinity of ${T}_{c}.$ The single vortex structure is studied by solving the GL equations. The asymptotic form of the order parameter for large $r$ is proportional to ${e}^{if(\ensuremath{\theta})}$ instead of ${e}^{i\ensuremath{\theta}}$ where $f(\ensuremath{\theta})$ is a function of the anisotropy parameter. Near and far away from the vortex core, both $s$- and $d$-wave components exhibit a twofold symmetry. As the temperature is sufficiently close to ${T}_{c},$ the $s$-wave component exhibits almost the same behavior as the $d$-wave one. From the solution near the vortex core, we give a criterion for the appearance of the $s$-wave off-center vortices.