Time-Dependent Ginzburg-Landau Equation for d_{x^2 - y^2 } -wave Superconductors: Hall Effect in the Low Field Regime

The Hall effect is studied by using a phenomenological time-dependent Ginzburg-Landau equation with mixing of s-and d-wave components in -wave superconductors within a low field regime. An equation of motion for a single vortex is derived and the Hall angle is obtained under an external driving current along the crystal axis. We find that not only the imaginary parts of s- and d-wave relaxation time but also the mixed gradient terms may change the sign of the Hall effect.