Dynamics of d-wave Vortices: Angle-Dependent Nonlinear Hall Effect

We study the dynamics of vortices in d-wave superconductors using a phenomenological time-dependent Ginzburg-Landau equation with mixing of s- and d-wave components. We present numerical simulations under an external driving current $J$ oriented with an angle $\phi$ with respect to the $b$ crystal axis, calculating the vortex motion and induced electric fields for $\kappa=\infty$. We find an intrinsic Hall effect for $\phi\neq 0$ which depends as $\sim\sin(4\phi)$, and increases non-linearly with $J$.