Static and dynamical anisotropy effects in the mixed state ofd-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 ${\beta }_A$ 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 $H_{c2\mathrm{}}$ the fourfold symmetry of the crystal lattice causes asymmetric motions of particles and holes, resulting in a nonvanishing Hall current.