High Tc Superconductors in Magnetic FieldsT. P. Devereaux

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

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

High Tc Superconductors Discovered in 1986, Nobel Prize for Bednorz and Mller in 1987

Critical Current On the Rise

New Superconductor DevelopmentsFullerenes: Tc engineered to 117K.Iron becomes a superconductor under pressure.Plastic superconductor: polythiophene.DNA can be made superconducting.MgB2 changes our thinking (again).

Large Scale ApplicationsTop speed: 552 km/hrIn-place in Detroit.*US Navy: 5,000 HP**American Superconductor Corp.

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.

Small Devices? Magnetic Fields!H. Safar et al (1993)

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

Direct Vortex Imaging Using Scanning Tunneling Microscope

Animation: Increasing Magnetic FieldApply current: Lorentz force causes vortices to move -> Resistance!

Solution: Defects to Pin VorticesKrusin-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.

Animation: Pinning Moving Vortices

Problems to OvercomeHigh TCElastic string under tension F:Du2= kBTy(L-y)/FL ~ kBT/F String is floppier at higher T -> vortex liquid2) Planar Structurepancake vortices in layers weakly coupledDecreased string tension -> vortex decoupling

Molecular Dynamics SimulationsWidely 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 pcs and supercomputers (parallel).

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

Abrikosov Lattice Melting - > Vortex LiquidAt low T, lattice forms with defects.At higher T, lattice melts.

PinningAt low T, a few pins can stop whole lattice.At larger T, pieces of lattice shear away.

Pinning at low fieldsColumns of defects are effective at pinning vortices.But channels of vortex flow proliferate at larger fields.

Depinning vortex avalanche

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

Resistivity is smaller for splayed defects

Optimal angle for splaying

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

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