Superconductivity and YBa Cu O

winkwellmadeUrban and Civil

Nov 15, 2013 (3 years and 7 months ago)

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Michael Browne

11/26/2007

2 3 7
Superconductivity and YBa Cu O



Discovered by Paul Chu et al. at the
University of Houston in 1987.



Becomes superconducting at 92K.



Famous as the first material that becomes
superconducting at a temperature above
the boiling point of liquid nitrogen (77K).

2 3 7
YBa Cu O
Crystal Structure of YBCO


Oxygen
-
deficient Perovskite structure.


Why the
δ
?


The properties of YBCO are strongly
dependent on the oxygen content.


Superconducting


from 0 to 0.55.


Antiferromagnetic


semiconductor from


0.55 to 1.


Insulator at 1.

What is Superconductivity?


Discovered by Onnes in 1911.



When Hg is cooled below 4.2K, its
electrical resistance drops to zero.




What is Superconductivity?


Characterized by an energy gap.


If electrons do not lose energy through
interactions with the lattice, it is because
they cannot.


If the interaction energy is smaller than the
energy gap, the electrons must stay in
their current energy state: so no
dissipation!

Type I Superconductors


Below critical field H
C
, no penetration of
magnetic flux (the Meissner effect).


H
C

decreases with increasing temperature,
until the critical temperature, T
C
.


Type II Superconductors


Below a lower critical field H
C1
, no
penetration of magnetic flux.


Above an upper critical field H
C2
, normal
penetration of magnetic flux.


In between these limits,


partial penetration of


magnetic flux.


The Meissner Effect


More than a simple consequence of
perfect conductivity!



Perfect conductivity implies that Lenz’ Law
would insure that magnetic fields remain
constant


not necessarily zero.



The Meissner Effect


Electromagnetic free energy is minimized
if the
London equation

is satisfied:





Maxwell’s Equations:


2
s
n e
j B
mc
  
4
B j
c

 
The Meissner Effect


As a consequence,




This implies that magnetic fields die off
exponentially within a superconductor!

2
2
2
4
s
n e
B B
mc

 
1/2
2
2
4
s
mc
n e


 

 
 
Penetration Depth of YBCO


Anisotropic!





The superconductivity
is mainly related to
the copper planes.



150nm
ab


800nm
c


BCS Theory


Electrons deform the lattice as they pass.


The deformation propagates as well: it is a
phonon!


Electron
-
phonon interactions result in the
formation of “Cooper pairs”.


BCS Theory


Electrons forming a pair act as a boson, so
many pairs can be in the same state.




Electron pairs have a characteristic size,
called the
coherence length
, .


Coherence Length of YBCO


Also anisotropic:





Coherence length is
small compared to
metal superconductors.


2nm
ab


0.4nm
c


Type II Superconductors


Penetration of flux is in the form of
filaments or vortices (Abrikosov).


Core is in normal


phase, surrounded


by a supercurrent.


Type II Superconductor


Magnetic flux is quantized! (quantum )


Field associated with a core penetrates
the superconductor to depth , so at the
minimum penetrating field:



Cores can be packed no tighter than , so
at breakdown point:


2
1 0
C
H

 
0


2
1 0
/
C
H

  

2
2 0
C
H

 
2
2 0
/
C
H

  
Type I vs. Type II


The relative size of and determines
the type of the superconductor!



implies superconductivity
breaks down before flux penetrates.



implies that flux can penetrate
and breakdown occurs later.



 
 
Type of YBCO







Clearly Type II!

2nm 150nm
ab ab
 
 
0.4nm 800nm
c c
 
 
Vortex Phase in YBCO



What Makes YBCO Superconduct?


Mechanism is currently unknown.



Some evidence that electron
-
phonon
interactions play a part. (Isotope studies)



Some evidence that Cooper pairs of a
different type are formed in high T
C

superconductors.


Symmetry of Cooper Pairs


In BCS theory, the wave function of a
Cooper pair is spherically symmetric. It is
said that they form an
s
-
wave state
.



A small ring of an ordinary superconductor
will trap a magnetic field. The flux inside
the ring will always be an
integer multiple

of the flux quantum.


Symmetry of Cooper Pairs


In YBCO, experiments have been done
which trap a
half
-
integer

flux quantum.



This implies the


underlying symmetry


is different. It is said


that the electrons


form a
d
-
wave state
.


The Future


What mechanisms could cause a d
-
wave
state?


“spin wave”



Can practical devices be built from YBCO?


YBCO is rather brittle.


Only pure crystals have high critical current
density.

Credits


Slide 1
http://en.wikipedia.org/wiki/YBCO


Slide 3, 12, 15
http://www.tkk.fi/Units/AES/projects/prlaser/material.htm

(edited)


Slide 4
http://www.ornl.gov/info/reports/m/ornlm3063r1/fig16.gif



Slide 5, 13
http://superconductors.org


Slide 7, 8
http://www
-
unix.mcs.anl.gov/superconductivity/phase.html


Slide 16, 20
http://www.fys.uio.no/super/vortex/


Slide 23
http://www.research.ibm.com/halfvortex/