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.
Highlights
One of the most interesting aspects of superconducting systems is the physics of vortices
We theoretically investigate the effect of finite size on the properties of vortices with numerical simulations of solutions of the time-dependent Ginzburg-Landau (TDGL) equations
The flux-flow Hall effect in square planar type-II superconductors is studied for different sample sizes, given by l/ξ ratio of 3, 5, 15, 20, 100, and 200
Summary
One of the most interesting aspects of superconducting systems is the physics of vortices. One may numerically compute the Hall effect in a superconducting sample governed by the modified TDGL system of Dorsey [12] and Kopnin et al [13], and find the magnetic field regimes of sign reversal. This could provide insights into Hall effect behavior of a superconductor as a function of macroscopic quantities alone (e.g., GL parameter κ, sample size, etc.). We find that transient electric fields and related order parameter behavior give us good insight into explaining the anomalous Hall effect
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