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

• 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 solvedproblem 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 liquidthat needs to be excited collectively(and thus obey a different statistic – ‘Fermi Liquid’)- at Tc energy gap , BCS value 3.52 kBTc = 2 - 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 - HTSC-Organic SC - ladder compounds

Today SC is perhaps the least understood phenomenonin Condensed Matter Physics. (‘Phase diagram’ of theories)

Un-explained Phenomena

Mediation process e- -phonon? e- - e- ?

Energy gap symmetry s-wave? d-wave? p-wave?

Energy gap nature spin-gap pseudo-gap

Origin of SC out of all things emerging fromAFM ???

Nature of coupling FL non-FL

Limit for Tc unknown, nobody knows how tocalculate

Electronic Structure

Transport Probes

• 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

• 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 e-

or in bad need for calibration to be quantitative

ARPES

Problems: photocurrent is very complicated quantity : surface sensitive probe

Advantage: momentum and frequency resolved probecomparable only to ineleastic n-scattering

Shine photons of specific energy on sampleIf E > work function, e- will be emittedE is measured and tells about initial E in crystal

Tunneling Spectroscopy

Advantage: Direct measurement of sc DOS

Problems: Surface technique

Neutron Scattering

Advantage: momentum and frequency resolved probe

Problems: Needs large single crystalsrequires n reactor (measuring time)measures a complicated functionwide elemental sensitivity range

Nuclear Magnetic Resonance

Advantage: solid theoretical understanding

wide variety of methodologytests bulk*dynamic (relaxation) and static (shift) probe

Problems: wide elemental sensitivity rangerequires magnetic field

Well understood behavior for metals:As function of temperatureAs function of magnetic fieldAs function of pressure

NMR HTSC:pseudo-gap

gap symemtry

gap size

New models of SCwhich 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 FLvsCoulomb repulsion b/w e-

which favors insulating magneticor 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