High Tc Superconductors
in Magnetic Fields
T. 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 1972
Most 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 Müller in 1987
Critical Current On the
Rise
New Superconductor
Developments
• Fullerenes: 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
Applications
Top speed: 552 km/hr
US Navy: 5,000 HP*
In-place in Detroit.*
*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!
Resistance
reappears!
<- Resistivity
of Pure
Copper
• 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 Field
Apply current: Lorentz force causes
vortices to move -> Resistance!
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.
Animation: Pinning
Moving Vortices
Problems to Overcome
1) High TC
Elastic string under
tension F:
Du2= kBTy(L-y)/FL
~ kBT/F
2) Planar Structure
“pancake” vortices in
layers weakly coupled
Decreased string
tension -> vortex
decoupling
String is floppier at
higher T -> vortex
“liquid”
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 pcs
and supercomputers (parallel).
Molecular Dynamics
Simulations for Vortices
•
•
•
•
•
Vortices = 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 Liquid
At low T,
lattice forms
with “defects”.
At higher T,
lattice “melts”.
Pinning
At low T, a few
pins can stop
whole “lattice”.
At larger T,
pieces of
“lattice” shear
away.
Pinning at low fields
Columns 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
flow
But too much splaying and vortices
cannot accommodate to defects.
Resistivity is smaller for
splayed defects
Optimal angle for splaying
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,…).