# Presentation: 850704

## 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
-  _x0013_

## 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

## What‘s so unique about cuprates ?

-  They are the most quantum of the conducting oxides !

## Cu2+

- Cu2+

- spin  S = 1/2

- Cuprates  => CuO2 plane electronically relevant

- e.g. Parent compound: La2CuO4

*1 hole in 3d-e**g*

- Cu2+  *3d**9*

- Strong Coulomb interaction
- Mott Insulator, S = 1/2 2D Heisenberg Antiferromagnet
-  => A Highly Quantum System !

- CuO2-plane

- square lattice of Cu2+-ions

- O-octahedra

## Cu2+

- Cu2+

- CuO2-plane

- -hybridization

- Cu

- O

*2p*

- doped
- hole

- Holes in a CuO2 plane : Cu3+

*3d**x**2**- y**2*

- Same Symmetry for
-  Cu2+ & Cu3+ => highly
-     mobile holes

## 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

## LaNiO2

- LaNiO2

- Differing Results in LDA + U
-  Anisimov,Bukvalov & Rice PRB `99
-        get AFI similar 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?

-          Conclusion
- Nickelates are not promising !

## Cuprates : Clean vs. Dirty

- Is our view of the cuprates strongly  influenced
-  by the disorder intrinsic to many of the cuprates ?

## 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)

## 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

## Standard Phase Diagram of the High-Tc Superconductors

- Standard Phase Diagram of the High-Tc Superconductors

- Is this the correct phase diagram for clean cuprates ?

- doping holes

- 0

## Zero Field NMR on 

- Zero Field NMR on
- Multilayer Hg & Tl cuprates
- - Osaka group(Mukuda et al 06)

- Hole density  largest
-     on outer planes
- least on inner planes

## Coexisting uniform AF & SC order

- Phase Diagram with overlaopping
-  AF & SC regions => VMC Results
-  by Ogata,TK Lee etc

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

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

## STM Patterns on Na-CCOC   Kohsaka et al  Science 315,1380 `07

- +  Cu sites

- STM Patterns on Na-CCOC   Kohsaka et al  Science 315,1380 `07

- 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?

## 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)

## Theory of the STM    Y Chen,TMR & FCZhang PRL`07

- 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
**   ****.**** **

- Theory of the STM    Y Chen,TMR & FCZhang PRL`07

** **

- Na-CCOC

## 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

- — Yang,TMR & Zhang`06

- 

- M

## 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

## 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 ?

## <— CuO2    chains

- <— CuO2    chains

- <— Cu2O3 planes

- Sr14Cu24O41 — Tel. No. Compound

- 2-Leg Ladder Compounds with Cu2O3 - planes

- SrCu2O3

- — _x0014_| 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.
- • _x0013_Are there compounds with doped  Cu2O3 - planes similar to the many
-         cuprates with doped CuO2   planes and would this enhance Tc ?

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- 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’_x0008_/4
- U ≈  -J  + Coulomb
-              + el. ph
- Energy gain from singlet
- groundstate of an
- island  may be possible?

## Cuprates after 20 years are  still producing surprises and fascinating puzzles. 

-  =>  John Tranquada_x0008_