Size dependence in flux-flow hall effect using time-dependent ginzburg-landau equations

Abstract

We study the Hall effect in square, planar type-II superconductors using numerical simulations of time dependent Ginzburg-Landau (TDGL) equations. The Hall field in some type-II superconductors displays sign-change behavior at some magnetic fields due to the induced field of vortex flow when its contribution is strong enough to reverse the field direction. In this paper, we use modified TDGL equations which couple an externally applied current, and also incorporate normal-state and flux-flow Hall effects. We obtain the profile of Hall angle as a function of applied magnetic field for six different sizes (l×l) of the superconductor: l/ζ∈{3,5,15,20,100,200}. We obtain vastly different profiles for different size regimes, proving that size is an important parameter that determines Hall behavior. We find that electric field dynamics provide an insight into several anomalous features including a sign change of the Hall angle, and leads us to the precise transient behavior of the order parameter responsible for them.