1. 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)

2. 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?

3. 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

4. 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)

5. 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 from AFM ??? Nature of coupling FL non-FL Limit for Tc unknown, nobody knows how to calculate

6. Electronic Structure

7. Transport Probes • Resistivity • Susceptibility • Specific Heat • Thermopower

8. Resistivity

9. Susceptibility Measurement Induced sample (magn.) moments are time dependent  AC probes magnetization dynamics, DC does not

10. Specific Heat

11. Thermopower

12. 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

13. 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: photocurrent is very complicated quantity : surface sensitive probe Advantage: momentum and frequency resolved probe comparable only to ineleastic n-scattering

14. Tunneling Spectroscopy Advantage: Direct measurement of sc DOS Problems: Surface technique

15. 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

16. 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

17. NMR HTSC: pseudo-gap gap symemtry gap size

18. 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 FL vs Coulomb repulsion b/w e- which favors insulating magnetic or charged ordered states ‘stripes’ are such density-wave states (charge, spin)

19. 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

20. Pseudogap

21. Organic SC H Mori