high temperature superconductivity: the secret life of electrons in cuprate oxides
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High Temperature Superconductivity:
The Secret Life of Electrons in Cuprate Oxides
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Metals• Shiny• Smooth• Malleable• Carry current
(conduct electricity)
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Metals and Current
• V = IR• Resistance• Wires radiate power away
as heat• You pay for more
electricity than you receive!• Electrons “scatter” off
lattice, and lose energy
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Superconductors
• Carry current perfectly• Do not lose energy• Current in a loop will run forever• Expel magnetic fields (Meissner effect)
http://micro.magnet.fsu.edu
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Levitation
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Levitation
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How does it happen?
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MatterNo two pieces of matter may
occupy the same space at the same time
(Only half true)
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Two kinds of particles
Fermions (spin 1/2, 3/2, 5/2, etc.)
• Cannot occupy the same space at the same time
• Pauli exclusion principle
Antisocial
Bosons (spin 0, 1, 2, etc.)
• Can occupy the same space at the same time
All Follow the Crowd
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Electrons are Fermions
Pauli exclusion principle
Why most matter cannot occupy the same space at the same time
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BosonsCan occupy the same space at the same time
Photons are bosons lasers
Helium is a boson superfluidity
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Bose condensation
• At low temperature, bosons flock to the lowest level
• Very stable state!• Dissipationless flow• Superfluidity (Helium)• Superconductivity (metals at low
temperature)
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Superconductivity
• Pair electrons form bosons• Bosons condense into the lowest orbital• Quantum mechanics! Very stable state • Dissipationless current flow
Conventional Superconductivity
Based on an instability of the simple metallic state
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Superconductors Have Zero Resistance?
• Metals: electrons “scatter” off lattice and lose energy resistance
• Superconductor: electrons pair
• Bosonic electron pairs in lowest state already
• There’s no lower state for them to scatter into
• Same as why atoms are stable
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Conventional Superconductivity
• BCS Theory
• Instability of the metallic state
John Bardeen Leon Cooper Bob Schrieffer
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Cooper Pairing
• Electrons in Metal Can Pair via the lattice
www.superconductors.org
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Instability
Of A Tranquil Fermi Sea—
Broken Symmetry
BCS Haiku:
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http://www.eere.energy.gov/superconductivity/pdfs/frontiers.pdf
And then there was 1986
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A Ceramic Superconductor?
• Brittle
• Ceramic
• Not Shiny
• Not metallic
• Why do they conduct at all?
http://www.superconductivecomp.com/
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High Temperature Superconductors
YBCO7
LSCO
HgCuO
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High Temperature Superconductors
Copper Oxygen Planes
Other Layers
Layered structure quasi-2D system
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High Temperature Superconductors
Copper-Oxygen Planes Important
“Undoped” is half-filled
Oxygen Copper
Antiferromagnet
Naive band theory fails
Strongly correlated
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High Temperature Superconductors
Dope with holes
Superconducts at certain dopings
Oxygen Copper
T
x
AF SC
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Mysteries of High Temperature Superconductivity
• Ceramic! (Brittle)
• Not a simple metal
• Magnetism nearby (antiferromagnetism)• Make your own (robust)
http://www.ornl.gov/reports/m/ornlm3063r1/pt7.html
• BCS inadequate!
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Two Ingredients for Superconductivity
Pairing
Single Particle Gap
Condensation
Superfluid Density
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1.4X1033915MgB2
1022026K3C60
5X1022617.4BaKBiO
1020.90.8UBe13
2X10417.818.7Nb3Sn
6X1057.27.9Pb
TTc[K]Tpair[K]Material
BCS is a mean field theory in which pairing precipitates order
4238Y-123 (ud)
62104 Bi-2212 (od)
14090116Y-123 (op)
14055Y-123 (od)
6095220Bi-2212 (op)
83275Bi-2212 (ud)
2526Tl-2201 (od)
16080Tl-2201 (od)
91122Tl-2201 (op)
130133435Hg-1223 (op)
130108290Hg-1212 (op)
18096192Hg-1201 (op)
10020LSCO (od)
543858LSCO (op)
473075LSCO (ud)
TTc[K]Tpair[K]Material
Phase FluctuationsImportant in Cuprates
Emery, Kivelson, Nature, 374, 434 (1995)EC, Kivelson, Emery, Manousakis, PRL 83, 612 (1999)
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Tc and the two energy scales
superconductivity
T
T
Tpair
AF
x
BCS won’t work.
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Doped Antiferromagnets
Hole Motion is Frustrated
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Doped Antiferromagnets
• Compromise # 1: Phase Separation
• Relieves some KE frustration
Pure AF
HoleRich
Like Salt Crystallizing From Salt Water,The Precipitate (AF) is Pure
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Coulomb Frustrated Phase Separation• Long range homogeneity
• Short range phase separation
• Compromise # 2: mesoscale structure
• Patches interleave
• quasi-1D structure – stripes ?
HoleRich
HolePoor
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Ferrofluid confined between two glass platesPeriod ~ 1cm
Block copolymersPeriod ~ 4X10-8 m
Ferromagnetic garnet filmPeriod ~ 10-5 m
Ferromagnetic garnet filmFaraday effectPeriod ~ 10-5 m
Competition often produces stripes
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What’s so special about 1D?
solitons
Disturbances in 3D: dissipate as ~ 1/R2
Disturbances in 2D: dissipate as ~ 1/R
Disturbances in 1D: “dissipate” as ~ 1
Like the intensity of light
Like a stone thrownin a pond
Like a wave in a canal
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canal
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1D: Spin-Charge Separation
spin excitation
charge excitation
Spin Charge SeparationElectron No Longer Exists!
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Strong Correlation
• Real space structure
• Kinetic energy (KE) is highly frustrated
• System works to relieve KE frustration
• Look for KE driven pairing
Fermi Liquid
• k-space structure
• Kinetic energy is minimized
• Pairing is potential energy driven
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Kinetic Energy Driven Pairing?
superconductor metal
Individually, free energies minimized
Metal pairs (at a cost!) to minimize kinetic energy across the barrier
Proximity Effect
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Stripey Proximity EffectKinetic energy driven pairing in a quasi-1D superconductor
Metallic charge stripe acquires gap (forms pairs) through communication with gapped environment
Step 1: Pairing
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Stripe Fluctuations
Stripe fluctuationsEncourage Condensation
Step 2: Condensation
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Summary• Superconductivity
– Fermions pair to form Bosons
– Bosons condense superfluid
– Very stable phase of matter
– Zero resistance
• Conventional (BCS) superconductivity:
– Instability of the simple metallic state
• High Temperature Superconductors– Don’t follow BCS theory
– Ceramic – not metallic
– Stripes: new mechanism• Pairing by proximity
• Coherence by fluctuations Relieve kinetic energy frustration of strongly correlated system