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Superconductivity
Characterized by - critical temperature Tc
- sudden loss of electrical resistance
- expulsion of magnetic fields
(Meissner Effect)
Type I and II superconductivity (vortices)
Above a critical magnetic field sc collapses
(much larger for type II SC)
Technological Importance
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Lossless energy conduction
Miniaturization (downtown & in space)
Effective Transportation (MagLevs)
Strong Magnetic Fields (fusion, MRI)
Thin Film detector technology/nano-tech
Basic Research Importance
• Macroscopic Quantum Effect
• A basic state of all matter?
Theory of SC
Until 1986 SC was considered the one completely solved
problem of condensed matter physics.
BCS theory (Bardeen, Cooper, Schrieffer)
a QM many-body theory
- predicted Tc and a theoretical limit for Tc
- below Tc 2 cond. e- of opposite impulse and spin build
‘Cooper pair’ and correlate to a macroscopic liquid
that needs to be excited collectively
(and thus obey a different statistic – ‘Fermi Liquid’)
- at Tc energy gap D, BCS value 3.52 kBTc = 2 D
- mediation of process through e--phonon coupling
Validation of BCS Theory
-All known SC (elemental metals, alloys, compounds)
obeyed the law of max. Tc
-NMR experiments measured and confirmed
the energy gap
Late 1980s: Exotic SC emerges
In rapid succession several classes of SC were
discovered which did not obey BCS theory.
-Heavy Fermions
-Organic SC
- HTSC
- ladder compounds
Today SC is perhaps the least understood phenomenon
in Condensed Matter Physics. (‘Phase diagram’ of theories)
Un-explained Phenomena
Mediation process
e- -phonon? e- - e- ?
Energy gap symmetry
s-wave?
d-wave?
Energy gap nature
spin-gap
pseudo-gap
Origin of SC
out of all things emerging from
AFM ???
Nature of coupling
FL
Limit for Tc
unknown, nobody knows how to
calculate
p-wave?
non-FL
Electronic Structure
Transport Probes
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Resistivity
Susceptibility
Specific Heat
Thermopower
Resistivity
Susceptibility Measurement
Induced sample (magn.) moments are time dependent
 AC probes magnetization dynamics, DC does not
Specific Heat
Thermopower
Spectroscopic Probes
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Photoemission (esp ARPES)
Tunneling Spectroscopy
Neutron Scattering
NMR line shift
NMR relaxation
And all other spectrocopies like EPR, Moessbauer, Raman but these
are all less direct methods for probing eor in bad need for calibration to be quantitative
ARPES
Shine photons of specific energy on sample
If E > work function, e- will be emitted
E is measured and tells about initial E in crystal
Problems:
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photocurrent is very complicated quantity
surface sensitive probe
Advantage: momentum and frequency resolved probe
comparable only to ineleastic n-scattering
Tunneling Spectroscopy
Advantage: Direct measurement of sc DOS
Problems:
Surface technique
Neutron Scattering
Advantage: momentum and frequency resolved probe
Problems:
Needs large single crystals
requires n reactor (measuring time)
measures a complicated function
wide elemental sensitivity range
Nuclear Magnetic Resonance
Advantage: solid theoretical understanding
wide variety of methodology
tests bulk*
dynamic (relaxation) and static (shift) probe
Problems:
wide elemental sensitivity range
requires magnetic field
Well understood behavior for metals:
As function of temperature
As function of magnetic field
As function of pressure
NMR HTSC:
pseudo-gap
gap symemtry
gap size
New models of SC
which try to address the new phase diagrams
Stripes (charge order)
Approach: how does a Mott Insulator
(ie a substance which should have been
a conductor but isn’t) turn into a SC?
Kinetic energy favors FL
vs
Coulomb repulsion b/w ewhich favors insulating magnetic
or charged ordered states
‘stripes’ are such density-wave states
(charge, spin)
RVB vs QCP
QCP – continuous phase transition at T=0[K]
driven by zero-point q fluctuations b/c of uncertainty relation
RVB – coherent singlet ground state
Pseudogap
Organic SC
H Mori

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