1. Michael Browne
11/26/2007

2. 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).

3. Crystal Structure of YBCO
Oxygen-deficient Perovskite structure.

4. 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.

5. What is Superconductivity?
Discovered by Onnes in 1911.
When Hg is cooled below 4.2K, its electrical resistance drops to zero.

6. 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!

7. Type I Superconductors
Below critical field HC, no penetration of magnetic flux (the Meissner effect).
HC decreases with increasing temperature, until the critical temperature, TC.

8. Type II Superconductors
Below a lower critical field HC1, no penetration of magnetic flux.
Above an upper critical field HC2, normal penetration of magnetic flux.
In between these limits,
partial penetration of
magnetic flux.

9. 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.

10. The Meissner Effect
Electromagnetic free energy is minimized if the London equation is satisfied:
Maxwell’s Equations:

11. The Meissner Effect As a consequence,
This implies that magnetic fields die off exponentially within a superconductor!

12. Penetration Depth of YBCO
Anisotropic!
The superconductivity is mainly related to the copper planes.

13. 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”.

14. 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, .

15. Coherence Length of YBCO
Also anisotropic:
Coherence length is small compared to metal superconductors.

16. Type II Superconductors
Penetration of flux is in the form of filaments or vortices (Abrikosov).
Core is in normal
phase, surrounded
by a supercurrent.

17. 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:

18. 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.

19. Type of YBCO
Clearly Type II!

20. Vortex Phase in YBCO

21. 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 TC superconductors.

22. 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.

23. 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.

24. 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.

25. Credits Slide 1 http://en.wikipedia.org/wiki/YBCO
Slide 3, 12, 15 (edited)
Slide 4
Slide 5, 13
Slide 7, 8
Slide 16, 20
Slide 23