Size Dependence in Flux-Flow Hall Effect using Time-Dependent Ginzburg-Landau Equations

TL;DR

This study uses numerical simulations of time-dependent Ginzburg-Landau equations to explore how the size of square type-II superconductors influences the flux-flow Hall effect, revealing size-dependent behaviors and sign changes in the Hall angle.

Contribution

The paper introduces a modified TDGL model that incorporates size effects and flux-flow Hall effects, providing new insights into size-dependent Hall behavior in superconductors.

Findings

Hall angle profiles vary significantly with superconductor size

Size is a key parameter influencing Hall effect behavior

Electric field dynamics explain sign changes in Hall angle

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 work, 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 four different sizes (l\times l) of the superconductor: l/ \xi belongs to {3, 5, 15, 20}. We obtain vastly different profiles for each size, proving that size is an important parameter that determines Hall behavior. We find that electric field dynamics provides an insight into several anomalous features including signchange of Hall angle, and leads us to the precise transient behavior of order parameter responsible for them.