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

TL;DR

This paper investigates how vortices in d-wave superconductors move and generate electric fields under various angles and currents, revealing an intrinsic angle-dependent Hall effect that varies with the sine of four times the angle.

Contribution

It introduces a phenomenological model combining s- and d-wave components to simulate vortex dynamics and uncovers an intrinsic, angle-dependent nonlinear Hall effect.

Findings

Intrinsic Hall effect depends on the angle as sin(4φ).

Hall effect increases non-linearly with the external current J.

Vortex motion and electric fields are characterized for different orientations.

Abstract

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 $J$.