Nanophysics in superconductivity
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BCS-theory
Flux vortices
Josephson junction
Coherence length
Knut Tyse
BCS - theory
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The basis for S.C. quantum theory
Two and two electrons form cooper pairs
Wavevector is
or
Wavefunction of cooperpair:
• Not the only configuration
Coherence length
A meashure of the spatial variation of
the density of superconducting
electrons.
A small coherence length means that
the density changes rapidly.
Intrinsic coherence length:
Or by using BCS-quantum-theory:
is the energy gap needed to destroy superconductivity while
the fermi velocity.
For alloys and impure superconductor we have
For a «dirty» material we have
is
The coherence length is a meashure of
transition-length between normal and
superconducting domains.
Flux quantization
• Magnetic flux vortices are quantized in
Figure:
http://www.physics.umd.edu/courses/Phys726/The_Quantum_Vortex.htm
At saturation
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.
• Then the normal cores are a distance
appart.
• This means that the sample becomes normal
at
.
Josephson junctions (JJ)
The superconductor (S) is interrupted by a thin
barrier (B) (Not to scale in the figure)
• The barrier can be
- an insulator (oxide layer) , 1-2 nm
- a material which is not a S.C.
- a point where the S.C material is much
thinner.
- a grain boundary if is small
• The key is to have a weak link between the
S.C.s
• The thickness of the weak link must be
tailored
Two theoretical predictions
1:
• The tunnel junction will be superconducting
up to .
2:
• If
the junction will radiate EM-waves
with high frequency
Nobel prize 1973
• Brian David Josephson
- theoretical prediction
• Leo Esaki and Ivar Giæver
- experimental discovery
Quantum mechanics explains this
Bose condensate:
2 and 2 electrons can form cooperpairs.
In a material every cooperpair shares the
same wavefunction and energy
The cooperpairs in S1 and S2 have equal
amplitude in the wavefunction.
However they have arbitrary phase.
Now: Introduce the weak link
• The weak link acts as a
perturbation
• It does not drastically
change the wavefunctions
in S1 and S2.
• Interference between S1
and S2 creates a new
wavefunction across the
system.
DC effect
• Start with wavefunctions:
• Write the Schrödinger equation for
and
• Solving gives a solution for the current
through the barrier:
AC-effect:
Apply a
voltage
accross the
junction
BIB
IIIII
DOS- vacant states
Cooper pairs at
fermi level
Cooper pairs at
fermi level
DOS filled states
http://en.wikipedia.org/wiki/Superconducting_tunnel_junction
Result for AC Josephson effect
Is an integration constant
The current oscillates with frequency
Photons with energy
Can determine the value of
very precisely
can be emitted/absorbed
Sources
http://eu.wiley.com/WileyCDA/WileyTitle/productCd-EHEP000803.html
http://books.google.no/books/about/The_Physics_of_Superconductors.h
tml?id=8O8svNo_tWoC&redir_esc=y