Static and dynamical anisotropy effects in the mixed state of d -wave superconductors

We describe the effects of anisotropy caused by the crystal lattice in d-wave superconductors using an effective free-energy approach in which only one order parameter, the d-wave order-parameter field, is used. The Abrikosov parameter βA is calculated analytically for both static and moving vortex lattices. The analytic expression provides an unambiguous determination of the vortex-lattice structure. We also calculate both direct and Hall I-V curves as functions of the angle between the current and the crystal-lattice orientation. In particular, we show that near Hc2 the fourfold symmetry of the crystal lattice causes asymmetric motions of particles and holes, resulting in a nonvanishing Hall current.