Computational Approaches to High Temperature Superconductors ...

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15 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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High T
c
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 T
c

Superconductors
Discovered in 1986, Nobel Prize
for Bednorz and M
ü
ller in 1987

Critical Current On the
Rise


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).

Large Scale

Applications

Top speed: 552 km/hr

In
-
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)

<
-

Resistivity
of Pure
Copper

Resistance
reappears!

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 T
C

Elastic string under
tension F:

D
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

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).

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,…).