Superconductivity Characterized by- critical temperature T c - 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 solved problem of condensed matter physics. BCS theory (Bardeen, Cooper, Schrieffer) a QM many-body theory - predicted T c and a theoretical limit for T c - below T c 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 T c energy gap , BCS value 3.52 k B T c = 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 phenomenon in Condensed Matter Physics. (‘Phase diagram’ of theories)

Un-explained Phenomena Mediation processe - -phonon? e - - e - ? Energy gap symmetrys-wave?d-wave?p-wave? Energy gapnaturespin-gappseudo-gap Origin of SCout of all things emerging from AFM ??? Nature of couplingFLnon-FL Limit for T c unknown, nobody knows how to calculate

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 probe comparable only to ineleastic n-scattering 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

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 e - which 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