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

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+

spin S = 1/2

Cuprates => CuO2 plane electronically relevante.g. Parent compound: La2CuO4

eg

t2g

x2-y2

3z2-r2

yzzxxy

1 hole in 3d-eg

Cu2+ 3d9

Strong Coulomb interaction

Mott Insulator, S = 1/2 2D Heisenberg Antiferromagnet

=> A Highly Quantum System !

CuO2-plane

O

Cu

square lattice of Cu2+-ions

O-octahedra

doped holes enter the O-2p orbitals and form Z-R singlets

Cu2+

2px

2py

3dx2

- y2

€

H = −t (c is+

i, j ,s

∑ c js + hc.) + Jr S i

i, j

∑ ⋅r S j

t-J-model: motion of holes in AF background

CuO2-plane

-hybridization

Cu O

2p

dopedhole

singlet

Holes in a CuO2 plane : Cu3+

3dx2

- y2

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

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?

ConclusionNickelates 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

AFSC

T

x

TN

Tc

T*

under optimally overdoped

spin gapSpinglass

strangemetal

Is this the correct phase diagram for clean cuprates ?

doping holes

0

Zero Field NMR on Multilayer Hg & Tl cuprates

- Osaka group(Mukuda et al 06)

Hole density largest on outer planesleast 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

+ 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)

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

<— Cu2O3 planes

Sr14Cu24O41 — Tel. No. Compound

2-Leg Ladder Compounds with Cu2O3 - planes

SrCu2O3

— | 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 ?

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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’/4

U ≈ -J + Coulomb + el. ph

Energy gain from singletgroundstate of an island may be possible?

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

=> John Tranquada