On the Fourfold Symmetry ofHc2and Magnetization ofdx2-y2-Wave Superconductors for the in-Plane Magnetic Fields

Abstract

For the d x 2 - y 2 superconductors, we investigate the fourfold symmetry of the upper critical fields and magnetization related to the torque under the parallel magnetic field to the a b plane of the crystal. We take into account the s -wave order parameter induced from the spatial variation of the d x 2 - y 2 -wave order parameter. In addition, we investigate the effects of the shape of the Fermi surface. If the pairing interaction for the s -wave channel is attractive, the s -wave component can enhance the above fourfold symmetry. Depending on the structure of the Fermi surface, the fourfold symmetric anisotropy in the a b plane enhances or suppresses the fourfold symmetric behavior. There is also the case where the fourfold symmetric anisotropy of in the a b plane changes the sign of the fourfold symmetric behavior from that of the isotropic case.