1. High T c Superconductors in Magnetic Fields T. P. Devereaux

2. Kamerlingh Onnes, 1913 Nobel Prize for Discovery of Superconductivity in Mercury

3. Theory of Superconductivity by Bardeen, Cooper, and Schrieffer Earns Nobel Prize in 1972 Most successful many-body theory. Quantum Coherent State “paired” electrons condense into coherent state -> no resistance. “paired” electrons condense into coherent state -> no resistance. perfect diamagnetism – electrons circulate to screen magnetic field (Meissner effect). perfect diamagnetism – electrons circulate to screen magnetic field (Meissner effect).

4. High T c Superconductors Discovered in 1986, Nobel Prize for Bednorz and Müller in 1987

5. Critical Current On the Rise

6. New Superconductor Developments Fullerenes: T c engineered to 117K. Iron becomes a superconductor under pressure. Plastic superconductor: polythiophene. DNA can be made superconducting. MgB 2 changes our thinking (again).

7. Large Scale Applications Top speed: 552 km/hr In-place in Detroit.* US Navy: 5,000 HP* *American Superconductor Corp.

8. Small Scale Devices?   Transistors (RSFQ peta-flop supercomputer)?   Filters?   Nano-scale motors and devices?   Superconducting DNA?   Quantum computers!? OBSTACLES: cooling. architecture. ever-present magnetic fields destroy coherence. ever-present magnetic fields destroy coherence.

9. Small Devices? Magnetic Fields! H. Safar et al (1993) <- Resistivity of Pure Copper Resistance reappears!

10. Problem: Vortices! Electrons swirl in magnetic field – increased kinetic energy kills superconductivity. SOLUTION: Magnetic field kills superconductivity in isolated places -> VORTICES (swirling “normal” electrons)

11. Direct Vortex Imaging Using Scanning Tunneling Microscope

12. Animation: Increasing Magnetic Field Apply current: Lorentz force causes vortices to move -> Resistance!

13. Solution: Defects to Pin Vortices Krusin-Elbaum et al (1996). Critical current enhanced by orders of magnitude over “virgin” material. Splayed defects better than straight ones. Optimal splaying angle ~ 5 degrees.

14. Animation: Pinning Moving Vortices

15. Problems to Overcome 1)High T C Elastic string under tension F:  u 2 = k B Ty(L-y)/FL ~ k B T/F String is floppier at higher T -> vortex “liquid” 2) Planar Structure “pancake” vortices in layers weakly coupled Decreased string tension -> vortex decoupling

16. Molecular Dynamics Simulations Widely used for a variety of problems: - protein folding, weather simulation, cosmology, chaos, avalanches, marine pollution, other non-equilibrium phenomena. Solves equations of motion for each “particle”. Large scale simulations on pc s and supercomputers (parallel).

17. Molecular Dynamics Simulations for Vortices Vortices = elastic strings under tension.Vortices = elastic strings under tension. Vortices strongly interact (repel each other).Vortices strongly interact (repel each other). Temperature treated as Langevin noise.Temperature treated as Langevin noise. Solve equations of motion for each vortex.Solve equations of motion for each vortex. Calculate current versus applied Lorentz force, find what type of disorder gives maximum critical current.Calculate current versus applied Lorentz force, find what type of disorder gives maximum critical current.

18. Abrikosov Lattice Melting - > Vortex Liquid At low T, lattice forms with “defects”. At higher T, lattice “melts”.

19. Pinning At low T, a few pins can stop whole “lattice”. At larger T, pieces of “lattice” shear away.

20. Pinning at low fields Columns of defects are effective at pinning vortices. But “channels” of vortex flow proliferate at larger fields.

21. Depinning vortex avalanche

22. Splayed defects effective at cutting off channels of vortex flow But too much splaying and vortices cannot accommodate to defects.

23. Resistivity is smaller for splayed defects

24. Optimal angle for splaying

25. Acknowledgement & Future Work All simulations performed by Dr. C. M. Palmer. Complex vortex dynamics. Future work to investigate –Melting phenomena. –Oscillatory motion of driven vortices. –Onset of avalanches. –Behavior as a qubit (quantum computing). –Behavior of other dual systems (polymers, DNA,…).