1. Encounters with Oxides - Wins and Losses - Maurice Rice ETHZ & HKU - A Look back to the Sixties - New Physics in Oxides - High-T c Cuprate Oxides - The Big Surpise that continues - Future Prospects

2. The CAT and the CREAM I might remark that in low-temperature physics the disappearance of liquid helium, superconductivity, and magneto-resistance from the list of unsolved problems has left this branch of research looking pretty sick from the point of view of any young innocent who thinks he is going to break new ground. A. B. Pippard Physics Today, 1961 The last generation of settlers in the new land of Physics found it green and fertile; we shall leave it a dustbowl.

3. Even number of electrons/unit cell Band picture - electrons in momentum space electrons in a periodic potential form Bloch waves and energy bands Bloch waves Energy eigenvalues Odd number of electrons/unit cell E metal insulator semiconductor E energy gap Repulsive interaction between electrons is a perturbation Fermi sea Fermi liquid of “independent” Quasiparticles (Landau, 1956) Insulator, Semiconductor Metal

4. Cooper Pairs of electrons formed by an attraction Conventional Superconductivity Conventional pairing angular momentum l =0 spin singlet B ardeen C ooper S chrieffer ‘ 57 Specific Heat C(T) vanishes exponentially as T ->0 Pairing Amplitude constant around Fermi Suface Energy gap also constant Macroscopic Coherent Pair Wavefunction forms for T<Tc : analagous to a Bose-Einstein Condensate of bosons BCS Theory explains all features of conventional superconductors Attractive interaction through electron-phonon interaction

5. Where did Pippard go wrong ? Some Examples - Semiconductors -> Artificially Structured Materials led to new devices & new physics e.g. Quantum Hall Effect - Metals -> New Compounds led to new physics e.g. Oxides with strongly interacting electrons which show new properties - Hi-T c supeconductivity

6. V 2 O 3 : First Example of a Mott Transition between a Metal and Localized Insulator without a symmetry change McWhan,Rice `69

7. Atomic limit - electrons localized in real space Lattice of H-Atoms:a B << d e-e - repulsion: U = E(H + ) + E(H - ) Electrons localized : Mott Insulator Low-energy physics purely due to electron spins antiferromagnetic spin order generally at low T H+H+ H-H- H 2a B d -t S=1/2 STRONG Fundamentally different from a band insulator > 2zt

8. Metallic State shows Landau Fermi Liquid Behavior No Superconductivty alas! - just an enhanced effective mass m* Brinkman - Rice Theory (1970) The Fermi Surface of a metallic state disappears thru ‘ a diverging m* as the Mott insulator is approached -> neglects J (AF Interactions) works beautifully in 3 He ( Infinite U)

9. „ High- T c “ S uperconductivity in a oxide near a Metal-Insulator Transition Sleight et al `75 T c = 10K at x=0.3 Insulator is a CDW with Bi +3 & Bi +5 sites melting of el. Pairs leads to Superconductivity - Rice&Sneddon `81 - Yoshioka-Fukuyama `85

10. Interpenetrating s.c. lattice of X and O ions XO (1D), XO 2 (2D) & XO 3 (3D) O 2- - Ion Displacement Pattern in 2D is unfrustrated ! Result : A Charge Density Wave in BaBiO 3 i.e. 2 Sublattices with Bi 3+ & Bi 5+ ions leading to an energy gap in the Bi-6s band

11. G. Bednorz & K.A. Müller (La/Ba) 2 CuO 4 YBa 2 Cu 3 O 7 C.W. Chu & M.K. Wu MgB 2 Superconductivity T c over time

12. But we started from the wrong groundstate ! La 2 CuO 4 is an Antiferromagnetic not a CDW Insulator First Idea : The CuO 2 -planes are similar to the BiO 3 lattices

13. Doping a CDW insulator leads to a Superconductor but T c is low ! Better Example: Ba 1-x K x BaO 3 Mattheiss et al,Cava et al, Hinks et al `88 Reason is that CDW state is much more stable than AF state ! T c CDW = E F e 1/(  T N =const. J

14. High Temperature Superconductivity CuO 2 plane Copper-oxide compounds 1986: J.G. Bednorz & K.A. Müller La 2-x Ba x CuO 4 T c =35 K AF SC T x TNTN TcTc T* Doped antiferromagnetic Mott insulator under optimally over doped spin gap strange metal Tc up to 133K Schilling & Ott ‘93 Are they unconventional superconductors? Not ordinary metals! Generic Phase Diagram

15. ^Tc^Tc Singlet Pairing of Cu 2+ -Spins in the Pseudogap Phase Well Ordered and Underdoped - Continuous Onset of Spin Pairing in Normal Phase - Spin Susceptibility well below AF value at T ~ T c - Hole Doped Insulator in Pseudogap Phase YBa 2 Cu 4 O 8 Knight Shift ~ Spin Susceptibility Mali et al +...

16. New Powerful Experimental Tools : (Surface Sensitive) ARPES (Angle Resolved Photoemission Spectroscopy) Measures A(k,  ) = Im G(k,  ) - Shen, Campuzano, Fink, Johnston STM (Scanning Tunneling Spectroscopy) Measures local D.O.S. to add/remove an electron- Fischer, Davis Phase Sensitive Experiments to determine symmetry

17. Symmetry of Cooper Pairs Pair wavefunction: totally antisymmetric under electron exchange even parity odd parity S=0 singlet S=1 triplet L = 0,2,4,... L=1,3,5,… orbital spin Broken symmetries: U(1)-gauge symmetry Superconductivity Crystal deformation time reversal magnetism

18. Tsuei, Kirtley et al. (1995) Tri-Crystal Geometry Superconducting loop YBa 2 Cu 3 O 7 T c = 92 K = 60  m Tsuei-Kirtley frustrated loops SQUID-scanning-microscope measures the magnetic field that results from the current frustrated loops lead to a current in groundstate magnetic field Odd number of  -shifts

19. Basic model for doped cuprates Single 2D Mott band lightly doped with holes Mobile Holes and Interacting Spins t-J model: J/t = 1/3 Intrinsic strong coupling between hole motion and spin configuration makes it very difficult to analyse Cu 2+ : S=1/2 Zhang-Rice Singlet Cu 3+ : S=0

20. 2D RVB State which is a superposition of configurations with Singlet Pairs can be written as a projected BCS - State. Explains many features of Hi-T c - Anderson et al J Phys C ‘04 singlet Resonating Valence Bond Theory Doping allows singlets to move Proposed by Anderson ‘87 Singlet energy gain is 3x Classical energy

21. shows only Fermi arcs

22. K. M. Shen et al., Science 307, 901 (2005) pocket “FS” Comparison with ARPES experiments - Phenom. RVB Yang,Rice &Zhang ‘06

23. News & Views Nature 3 Aug 06 A.Cho Science 4 Aug 06 D.J.Scalapino Nature Physics News &Views Sept. `06

24. Examples of dI/dV spectra at various points on surface Peaks in in these spectra at a roughly const. energy  Simliar to those observed in classic superconductors e.g. Pb ?

25. BSSCO Surface in BiO layer but states at are in layer -> els tunnel thru`apical O ion. This can lead to emission of apical O-phonons. Tunneling Path in space & in energy with emission of  phonon Pilgram,Rice & Sigrist `06

26. Note Multiphonon Peaks at larger values of  El.-Phonon Coupling

27. Conclusions Phonon Sidebands in STM can arise from inelastic tunneling thru‘ apical O Spatial Anticorrelation between phonon energy and energy gap in STM spectra can arise from local variations in the structure of planes due to BiO superlattice, Bi:Sr nonstoichiometry etc Case for an Electron-Phonon Mechanism for High-Tc is unproven ! But have we reached the end of the road for BCS superconductors?

28. MgB 2 - a 21 st century high-temperature superconductor T c = 39 K (Akimitsu et al. 2001) 2D  -band dominant 3D  -band passive Isoelectronic to Graphite Moderately strong el.-ph. coupling to B-B mode Mazin,Andersen,Pickett & - -  Fermi Surface(green) difficult to obtain.

29. Prediction of a High - T c in a material with a  band Fermi Surface Rosner,Kitaigorodsky & Pickett `02 LiBC isoelectronic to MgB 2 is a semiconductor Can it be hole doped ? e.g. Li 1-x BC so far NO!

30. Future Prospects New Materials are still being discovered New Ideas on tailoring known materials may be a better way to go