用含时Ginzburg-Landau方程研究磁通流霍尔效应的尺寸依赖性
Size Dependence in Flux-Flow Hall Effect using Time-Dependent Ginzburg-Landau Equations
摘要：
本文利用含时的Ginzburg-Landau（TDGL）方程组数值模拟了方形平面第二类超导体中的霍尔效应。在某些第二类超导体中，由于涡流的感应场的作用，当它的贡献强到足以使场的方向反转时，在某些磁场中的霍尔场会出现符号变化。在这项工作中，我们使用修改后的TDGL方程耦合外部施加的电流，并纳入正常状态和磁通流霍尔效应。我们得到了四种不同尺寸（l \times l）的超导体的霍尔角随外加磁场的变化曲线：l/n属于{3，5，15，20}。我们获得了不同的配置文件为每个大小，证明大小是一个重要的参数，决定霍尔行为。我们发现，电场动力学提供了一个洞察到几个异常的功能，包括霍尔角的符号变化，并导致我们精确的瞬态行为的序参量负责他们。
英文摘要：
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/ ξbelongs 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.
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