Whither Strongly Correlated Electron Physics ? T.M.Rice ETHZ & BNL

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. x2-y2 3z2-r2 yz zx xy O eg t2g Cu Cuprates => CuO2 plane electronically relevant CuO2-plane e.g. Parent compound: La2CuO4 Cu2+3d9 Cu2+ 1 hole in 3d-eg O-octahedra spin S = 1/2 square lattice of Cu2+-ions Strong Coulomb interaction Mott Insulator, S = 1/2 2D Heisenberg Antiferromagnet => A Highly Quantum System !

5. 2px 2py singlet 3dx2- y2 doped holes enter the O-2p orbitals and formZ-R singlets t-J-model:motion of holes in AF background Holes in a CuO2 plane : Cu3+ CuO2-plane s-hybridization O Cu doped hole 2p Cu2+ 3dx2- y2 Same Symmetry for Cu2+ & Cu3+ => 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 Ni2+ 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 ? • Ni3+: No Good! 3 holes favor a 3d82p5 config. => metallic behavior e.g. LaSrNiO4 • Ni+ : Rare! Needs planar coordination as in LaNiO2

7. Differing Results in LDA + U • Anisimov,Bukvalov & Rice PRB `99 • get AFIsimilar to CaCuO2 • Lee & Pickett PRB `04 • get weakly AFM unlike CaCuO2 • Expt. Hayward et al J.Am.Chem. • insulator with Curie -Weiss  • S=1/2 & = - 257K; no AF order • Nonstoichiometric Mott • Insulator? LaNiO2 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 (a) Most Damage & (c) Least Damage Single Layer Bilayer Trilayer N.B. Cuprates with good surfaces are in (a) Hg & Tl Cuprates BSCCO & Na-CCOC

10. Ultra Clean Underdoped Cuprates ( No Intrinsic Disorder ) a) YBCO6.5 Ortho II - UBC group Alternate Chains with & without O b) YBa2Cu4O8 - Karpinski Double Cu-O-Cu Chains

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

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. STM Patterns on Na-CCOCKohsaka et al Science 315,1380 `07 + Cu sites 2 Features a) Rotational Symmetry of Cu4O4-square locally broken when tip is above O-sites but not Cu-sit b) Short Range Order with 4a0 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. Theory of the STMY Chen,TMR & FCZhang PRL`07 Na-CCOC STM tip couples to the outermost orbitals => 3pz 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 .

18. Quantum Oscillations in ultraclean underdoped Cuprates YBCO6.5 Ortho II Doiron-Leyraud et al `07 YBa2Cu4O8 - 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 M  — Yang,TMR & Zhang`06

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

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. 2-Leg Ladder Compounds with Cu2O3 - planes SrCu2O3 Sr14Cu24O41 — Tel. No. Compound <— CuO2 chains <— Cu2O3 planes — | 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 Sr14Cu24O41 which forms a hole pair xtal. • Are there compounds with doped Cu2O3 - planes similar to the many cuprates with doped CuO2 planes and would this enhance Tc ?

22. Pattern CuO2 with ZnO2 —> weakly coupled CuO2 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