s- and ${\mathit{d}}_{\mathit{xy}}$-wave components induced around a vortex in ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$-wave superconductors

The vortex structure of ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$-wave superconductors is microscopically analyzed in the framework of the quasiclassical Eilenberger equations. If the pairing interaction contains an s-wave (${\mathit{d}}_{\mathit{xy}}$-wave) component in addition to a ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$-wave component, the s-wave (${\mathit{d}}_{\mathit{xy}}$-wave) component of the order parameter is necessarily induced around a vortex in ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$-wave superconductors. The spatial distribution of the induced s-wave and ${\mathit{d}}_{\mathit{xy}}$-wave components is calculated. The s-wave component has an opposite winding number around the vortex near the ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$-vortex core and its amplitude has the shape of a four-lobe clover. These are consistent with results based on the Ginzburg-Landau (GL) theory. The amplitude of the ${\mathit{d}}_{\mathit{xy}}$ component has the shape of an octofoil. The mixing of the ${\mathit{d}}_{\mathit{xy}}$ component cannot be explained by the GL theory, unless nonlocal correction terms are included. © 1996 The American Physical Society.