For applications of superconductors it is important to control vortices. However, dynamics of vortices in a dirty super conductor under an external current is still not clean. For example, Nishida et al. showed vortices move as bundles separated by glide plane of dislocation. In order to clarify vortex dynamics ,we have developed “Molecular + Field Dynamics method.”
In a usual molecular dynamics (MD) method, an equation of motion for the i-th vortex is given by
where η is viscosity coefficient, ri is position of the vortex, fdi is a driving force by an external current, fpi is a pinning force due to an impurity potential, fvi is a repulsive force from other vortices, and ffi is a force due to thermal fluctuations.
In this method, we can only consider a few thousands vortices because of computation time of repulsive interactions between all points of vortices.
In order to treat more than ten thousands vortices, we consider a current field that consists of an external current and current around vortices.
The driving force from the external current and repulsive force from other vortices can be calculated locally as a current force fCi. Then the equation of motion becomes
The current field is obtained using the finite element method.In the simulations, a square superconductor was assumed, and the length of a piece was set to 5λ0 where λ0 is magnetic field penetration length.
Figure1 shows a vortex distribution from a simulation of 20000 vortices. Colors of vortices show direction of velocities of vortices.Using this method, we will show collective motions of vortices.
N. Nishida, K. Hirata, H. Takeda and H. Takeya, Physica C 470(2010)S795-S796
Keywords: Molecular dynamics method, Vortex, Finite Element method