1. Whither Strongly Correlated Electron Physics ? T.M.Rice ETHZ & BNL What`s so unique about the cuprates among the many materials with strongly correlated physics : e.g. transition metal oxides, heavy fermions, organic conductors.... Recent Experimental Advances & Surprises: Clean vs. Dirty Cuprates Experiments and Materials I would like to see

2. Special Features of Strongly Correlated Electrons Breakdown of Band Theory & Landau Theory of Fermi Liquids e.g. Mott insulators,pseudogap metallic phase etc Unconventional Superconductivty e.g. p- & d- wave and heavy fermion superconductors ? Novel Quantum Critical Points e.g. heavy fermion RKKY metal Multiple Electronic Phases in Close Proximity to each other e.g. magnetism & superconductivity etc. - - - - - - - - - - - Theoretical Challenges Strong Interactions => breakdown of perturbation theory etc Many Phases close by in energy e.g. AF,Stripe,d-SC &SF(?) order Microscopic Modelling can be difficult e.g. U compounds etc

3. What‘s so unique about cuprates ? They are the most quantum of the conducting oxides !

4. Cu 2+ spin S = 1/2 Cuprates => CuO 2 plane electronically relevant e.g. Parent compound: La 2 CuO 4 egeg t 2g x 2 -y 2 3z 2 -r 2 yz zx xy 1 hole in 3d-e g Cu 2+ 3d 9 Strong Coulomb interaction Mott Insulator, S = 1/2 2D Heisenberg Antiferromagnet => A Highly Quantum System ! CuO 2 -plane O Cu square lattice of Cu 2+ -ions O-octahedra

5. doped holes enter the O- 2p orbitals and form Z-R singlets Cu 2+ 2p x 2p y 3d x 2 - y 2 t-J -model : motion of holes in AF background CuO 2 -plane  -hybridization Cu O 2p doped hole singlet Holes in a CuO 2 plane : Cu 3+ 3d x 2 - y 2 Same Symmetry for Cu 2+ & Cu 3+ => highly mobile holes

6. Are there other planar S = 1/2 AF systems with larger values of (t,J) and so larger Tc ? Nickelates ? Favored valence is Ni 2+ with S =1 [ 2 holes,octa. coord. Cannot be doped with mobile holes & Hund`s Rule] Can we force a different Ni valence with S= 1/2 ? Ni 3+ : No Good! 3 holes favor a 3d 8 2p 5 config. => metallic behavior e.g. LaSrNiO 4 Ni + : Rare! Needs planar coordination as in LaNiO 2

7. LaNiO 2 Differing Results in LDA + U Anisimov,Bukvalov & Rice PRB `99 get AFI similar to CaCuO 2 Lee & Pickett PRB `04 get weakly AFM unlike CaCuO 2 Expt. Hayward et al J.Am.Chem.  insulator with Curie -Weiss   S=1/2 &  = - 257K; no AF order  Nonstoichiometric Mott Insulator? Conclusion Nickelates are not promising !

8. Cuprates : Clean vs. Dirty Is our view of the cuprates strongly influenced by the disorder intrinsic to many of the cuprates ?

9. Disorder in Cuprates Eisaki et al PRB 69,064512 (`04) Site of Disorder Single Layer Bilayer Trilayer (a) Most Damage & (c) Least Damage BSCCO & Na-CCOC Hg & Tl Cuprates N.B. Cuprates with good surfaces are in (a)

10. Ultra Clean Underdoped Cuprates ( No Intrinsic Disorder ) a) YBCO 6.5 Ortho II - UBC group Alternate Chains with & without O b) YBa 2 Cu 4 O 8 - Karpinski Double Cu-O-Cu Chains

11. Standard Phase Diagram of the High-T c Superconductors AF SC T x TNTN TcTc T* under optimally over doped spin gap Spin glass strange metal Is this the correct phase diagram for clean cuprates ? doping holes 0

12. Zero Field NMR on Multilayer Hg & Tl cuprates - Osaka group( Mukuda et al 06 ) Hole density largest on outer planes least on inner planes

13. Coexisting uniform AF & SC order Phase Diagram with overlaopping AF & SC regions => VMC Results by Ogata,TK Lee etc

14. VMC Results on t-J model - Himeda & Ogata PRB `99

15. + Cu sites STM Patterns on Na-CCOC Kohsaka et al Science 315,1380 `07 2 Features a) Rotational Symmetry of Cu 4 O 4 -square locally broken when tip is above O-sites but not Cu-sit b) Short Range Order with 4a 0 Domains Is the Pseudogap phase in underdoped cuprates an Intrinsic Electronic Glass?

16. No Sign of Charge Modulation on O - sites in an underdoped ultraclean cuprate NMR on O(2,3) planar sites Tomeno et al PRB (1994)

17. STM tip couples to the outermost orbitals => 3p z Cl When tip is above O-sites there can be interference between tunneling paths depending on relative phase to inject electrons thru’ nn Cl - ions. 1 hole bound to Na + acceptor can have a degenerate groundstate => Rotational symmetry breaking in STM pattern. Theory of the STM Y Chen,TMR & FCZhang PRL`07 Na-CCOC

18. Quantum Oscillations in ultraclean underdoped Cuprates YBCO 6.5 Ortho II Doiron-Leyraud et al `07 YBa 2 Cu 4 O 8 - Yelland et al `07  Small Fermi Pockets How many pockets in the BZ? In a Paramagnet ARPES predicts 4 => Too Many Holes ( x= 0.15 & 0.2) Underdoped Na-CCOC 1/4 of BZ — Yang,TMR & Zhang`06  M

19. If magnetic field induces AF long range order which reduces the Brillouin Zone ? => 2 Pockets => x= 0.075 & 0.1 Paramagnet AF order Chen et al `07 ARPES

20. Experiments I would like to see: ARPES & STM on clean and ultraclean cuprates Structured Cuprates => doped chains,ladders,islands, layered... New S=1/2 Materials with mobile carriers and different lattices : Organics ?

21. < — CuO 2 chains < — Cu 2 O 3 planes Sr 14 Cu 24 O 41 — Tel. No. Compound 2-Leg Ladder Compounds with Cu 2 O 3 - planes SrCu 2 O 3 — | 180º O-Cu-O Bonds form 2-leg ladders 2-leg AF S=1/2 Ladders form short range RVB spin liquids Holes form more stable pairs but 1D nature of ladders leads to competition between `d-SC and CDW ( hole pair xtals) Only doped example is Sr 14 Cu 24 O 41 which forms a hole pair xtal. Are there compounds with doped Cu 2 O 3 - planes similar to the many cuprates with doped CuO 2 planes and would this enhance T c ?

22. Pattern CuO 2 with ZnO 2 —> weakly coupled CuO 2 islands Can it lead to a U<0 Hubbard model when hole doped ? Cu Zn Interisland Hopping ≈ t’/4 U ≈ -J + Coulomb + el. ph Energy gain from singlet groundstate of an island may be possible?

23. Cuprates after 20 years are still producing surprises and fascinating puzzles. => John Tranquada