Encounters with Oxides - Wins and Losses - Maurice Rice ETHZ & HKU - A Look back to

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

2. The CAT and the CREAM A. B. Pippard Physics Today, 1961 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. The last generation of settlers in the new land of Physics found it green and fertile; we shall leave it a dustbowl.

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

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

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-Tc supeconductivity

6. V2O3 : First Example of a Mott Transition between a Metal and Localized Insulator without a symmetry change McWhan,Rice `69

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

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 in3He ( Infinite U)

9. „ High- Tc“ Superconductivity in a oxide near a Metal-Insulator Transition Sleight et al `75 Tc = 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) , XO2 (2D) & XO3 (3D) O2- - Ion Displacement Pattern in 2D is unfrustrated ! Result : A Charge Density Wave in BaBiO3 i.e. 2 Sublattices with Bi3+ & Bi5+ ions leading to an energy gap in the Bi-6s band

11. (La/Ba)2CuO4 YBa2Cu3O7 Superconductivity Tc over time MgB2 G. Bednorz & K.A. Müller C.W. Chu & M.K. Wu

12. First Idea : The CuO2 -planes are similar to the BiO3 lattices But we started from the wrong groundstate ! La2CuO4 is an Antiferromagnetic not a CDW Insulator

13. Doping a CDW insulator leads to a Superconductor but Tc is low ! Better Example: Ba1-xKxBaO3 Mattheiss et al,Cava et al, Hinks et al `88 Reason is that CDW state is much more stable than AF state ! TcCDW = EFe1/(TN=const. J

14. T TN T* CuO2 plane AF Tc SC x High Temperature Superconductivity 1986: J.G. Bednorz & K.A. Müller Tc up to 133K Schilling & Ott ‘93 Doped antiferromagneticMott insulator Generic Phase Diagram Copper-oxide compounds strange metal La2-xBaxCuO4 Tc =35 K spin gap under optimally over doped Are they unconventional superconductors? Not ordinary metals!

15. Singlet Pairing of Cu2+-Spins in the Pseudogap Phase Knight Shift ~ Spin Susceptibility YBa2Cu4O8 Well Ordered and Underdoped Mali et al + . . . ^ Tc • Continuous Onset of Spin Pairing in Normal Phase • Spin Susceptibility well below AF value at T ~ Tc • Hole Doped Insulator in Pseudogap Phase

16. New Powerful Experimental Tools : (Surface Sensitive) • ARPES (Angle Resolved Photoemission Spectroscopy) • Measures A(k,w) = Im G(k,w) - 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. totally antisymmetric under electron exchange S=0singlet even parity L = 0,2,4,... S=1triplet odd parity L=1,3,5,… Symmetry of Cooper Pairs Pair wavefunction: spin orbital Broken symmetries: U(1)-gauge symmetry Superconductivity Crystal deformation time reversal magnetism

18. = 60 mm Tsuei-Kirtley frustrated loops Odd number of p-shifts Tri-Crystal Geometry frustrated loops lead to a current in groundstate magnetic field Tsuei, Kirtley et al. (1995) SQUID-scanning-microscope measures the magnetic field that results from the current Superconducting loop YBa2Cu3O7 Tc = 92 K

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 Cu2+: S=1/2 Zhang-Rice Singlet Cu3+: S=0 Intrinsic strong coupling between hole motion and spin configuration makes it very difficult to analyse

20. Resonating Valence Bond Theory singlet Proposed by Anderson ‘87 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-Tc - Anderson et al J Phys C ‘04 Singlet energy gain is 3x Classical energy Doping allows singlets to move

21. shows only Fermi arcs

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

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

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

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

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. MgB2 - a 21stcentury high-temperature superconductor Tc = 39 K 2D -band dominant 3D -band passive (Akimitsu et al. 2001) Isoelectronic to Graphite Moderately strong el.-ph. coupling to B-B mode Mazin,Andersen,Pickett & - -  FermiSurface(green) difficult to obtain.

29. Prediction of a High - Tc in a material with a band Fermi Surface Rosner,Kitaigorodsky & Pickett `02 LiBC isoelectronic to MgB2 is a semiconductor Can it be hole doped ? e.g. Li1-xBC 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