Michael Browne 11262007 Discovered by Paul Chu et al. at the by dffhrtcv3


									Superconductivity and YBa 2Cu 3O 7

           Michael Browne
                YBa 2Cu 3O7

• 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).
    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
     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.
     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.
        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:
                  ns e
          j        B
• Maxwell’s Equations:
          B     j
         The Meissner Effect
• As a consequence,
            2  4 ns e      2
           B      2
• This implies that magnetic fields die off
  exponentially within a superconductor!
                                1/ 2
              mc      2
                   2 
              4 ns e 
Penetration Depth of YBCO
            • Anisotropic!
             ab  150nm
             c  800nm
            • The superconductivity
              is mainly related to
              the copper planes.
              BCS Theory
• Electrons deform the lattice as they pass.
• The deformation propagates as well: it is a
• 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:
               ab  2nm
              c  0.4nm
           • Coherence length is
             small compared to
             metal superconductors.
     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  0 )
• Field associated with a core penetrates
  the superconductor to depth  , so at the
  minimum penetrating field:
       H C1   0  H C1   0 / 
          2                                2

•   Cores can be packed no tighter than  , so
    at breakdown point:
       H C 2   0  H C 2   0 / 
          2                                 2
          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
•   ab  2nm 150nm  ab
    c  0.4nm 800nm  c
• Clearly Type II!
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 TC
    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
  – “spin wave”

• Can practical devices be built from YBCO?
  – YBCO is rather brittle.
  – Only pure crystals have high critical current
• 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/

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