| The transport properties of magnetic flux in layered superconductors and related mechanisms have attracted considerable attention in condensed matter physics.Using periodic boundary conditions in x and y directions and open boundary conditions in z direction,we studied the static and dynamic vortex distributions in 3D system at various pinning strength,obtained the dynamical characteristics and its singularity under the external driving force.As the closest model to real system is established by applying long periodic boundary conditions,we use reducing dimension and changing inter-vortex interaction methods to reduce heavy calculations without changing the model’s validity,and to study the properties of vortex pancake in layered superconductors and find the new explanation of the second peak effect.In recent years,vortex distributions in mesoscopic superconductor also became a hot topic.Unlike bulk superconductors,mesoscopic superconductors have small size,therefore the resulting vortex configurations are strongly depended on the sample shape and size.We mainly study isosceles right triangular mesoscopic superconductors.The main contents of this paper are as follows:We numerically studied the static configurations of pancake vortices in layered superconductors.We analyze how disordering induced by random pinning centers compete with inter-layer ordering and in-layer ordering.In general,for inter-layer ordering,3D states composed of coupled vortex lines are formed for strong inter-layer coupling strength and weak pinning strength.In the opposite,2D states composed of decoupled individual pancake vortices are formed for weak inter-layer coupling strength and strong pinning strength.For in-layer ordering,with increasing pinning forces,the in-layer structure involve from Crystals to Bragg Glasses(BG),Vortex Glasses(VG),and Liquid-like structures.Changing vortex density,a first fast disordering,then slowly ordering procedure is found for both in-layer and inter-layer ordering,which is a possible clue to second peak effects.The reason behind this non-monotonic behavior is discussed.Our results are summarized in a phase diagram in the plane of "inter-layer coupling strength Sm versus pinning strength fp.The dynamics of driven pancake vortices in layered superconductors is studied using molecular dynamics(MD)simulations.We found that,with increasing driving force,for strong inter-layer coupling,the pre-existed vortex lines either directly depin or they first transform to two-dimensional(2D)pinned states before they are depinned,depending on the pinning strength.In a narrow region of pinning strengths,we found an interesting repinning process,which results in a negative differential resistance(NDR).For weak inter-layer coupling,individually pinned pancake vortices first form disordered 2D flow,and then transform to ordered three-dimensional(3D)flow with increasing driving force.However,for extremely strong pinning,the random pinning induced thermal-like Langevin forces melt 3D vortex lines,which results in a persistent 2D flow in the fast sliding regime.In the intermediate regime,the peak effect is found:with increasing driving force,the moving pancake vortices first crystallize to moving 3D vortex lines,and then these 3D vortex lines are melted,leading to the appearance of a reentrant 2D flow state.Our results are summarized in a dynamical phase diagram.As the closest model to real system is established by applying long periodic boundary conditions,we use reducing dimension and changing inter-vortex interaction methods to reduce heavy calculations without changing the model’s validity,and to study the properties of vortex pancake in layered superconductors.For a reduced-dimensional system,it is no longer a triangular lattice of a three-dimensional system(or a traditional two-dimensional x-y plane),since the dimensions of the y direction are removed and the vortex pancakes are aligned in line paralleled to z direction.We calculated the correlation function of vortex’s steady state with different pinning strength and different layer numbers.With the increase of vortex density,we find the system is decoupled from the ordered 1D state to a disordered 2D state.The reason is that at high density,the lattice constant becomes smaller and the competition of the interaction potential will result in a decrease of the energy difference between the decoupled and the coupled states,which leading to a decoupled phase transition.This decoupling coincides with the experimental observed second peak effect.We numerically studied vortex configurations in mesoscopic superconducting isosceles right triangles.Using the Green’s function to find the analytical solution of London equation,we found the Gibbs free energy expression for an arbitrary configuration and performing molecular-dynamics simulations,obtained stable vortex configurations in the triangle.We find the filling rules for vortices:at low vorticity,the distribution of vortices are axisymmetric;with the increase of vorticity,asymmetric distribution began to appear;as increase the vorticity further,the distribution becomes more complex and diversity.As the system size increases,vortex patterns with a variety of metastable distribution appear at smaller vorticity,and the distribution of vortices is also more diverse.We compared vortex states in these two sizes of isosceles right triangles,and summarized all the stable states in a table. |
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