Vortex Dynamics in Type II Superconductors Yuri V. Artemov Yuri V. Artemov Ph.D. Student in Physics Brian B. Schwartz Mentor: Brian B. Schwartz Professor of Physics CUNY Fall 1998

Overview Properties of superconductors Two types of superconductors Theories of superconductivity Vortices in type II superconductors Interaction between vortices Interaction with defects Vortex dynamics Proposed research Vortices and computers Summary

Perfect conductor Properties of Superconductors Meissner effect Magnetic field destroys s/c  0 IcIc BcBc Electric current destroys s/c

Two Types of Superconductors Magnetization Magnetic Field Critical Field -4  M H HcHc H H c1 H c2 H B H c1 H c2 H B HcHc Type IIType I T HcHc TcTc Superconductor Normal Metal T HcHc TcTc Superconductor Normal Metal Mixed State

Theories of Superconductivity London Equation H BCS Theory Ginzburg-Landau Theory Electrons can attract via phonons Attraction leads to energy gap 1.76T c isotope effect EFEF EFEF 22 Normal Metal Superconductor

H r  Vortices in Type II Superconductors Magnetic Field j r  Current  r  Order Parameter

Interaction between Vortices B J FLFL Lorenz type force B B FLFL J Repulsion Triangular lattice

Interaction with Defects B J FLFL Flux Creep Activation energy behavior Pinning Vacancies, voids, inhomogeneities, where superconductivity is weak Pinning decreases energy losses caused by flux creep

Vortex Dynamics Collective behavior –Vortices interact strongly Effects of disorder –Interaction with pinning centers Many degrees of freedom –10 12 vortices in a sample Threshold dynamics –Can be driven to marginally stable state

Proposed Research Study the dynamics of vortices in type II superconductors  Given a superconductor with a certain pinning landscape, how do vortices move inside it?  How do microscopic pinning parameters affect measured macroscopic quantities?  How do vortices start moving when slowly driven towards the threshold of instability?  How to characterize dynamical instabilities in a superconductor?

Vortices and Computers  Vortices can be studied using computer simulations –A powerful theoretical tool to answer questions raised above –Allows to study phenomena hard to observe experimentally  Vortices can be effectively visualized using modern 3D design software –Making them more understandable to non-physics audience  Tools to be used –Powerful workstations at the CUNY New Media Lab –Softimage 3D software –DirectX technology with Visual C++ and Visual Basic –Matlab, Mathematica –Java & WWW

Summary 4General properties of superconductors 4Type I and type II superconductors 4Theories of superconductivity 4Vortices in type II superconductors 4Vortex interactions and dynamics 4Proposed research 4Using computers to study and visualize vortices