Whither Strongly Correlated Electron Physics T M

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 !

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

Holes in a Cu. O 2 plane : Cu 3+ Cu. O 2 -plane Cu shybridization O doped hole 2 p 3 dx 2 - y 2 singl Cu 2+ et Same Symmetry for Cu 2+ & Cu 3+ => highly mobile holes 2 px 2 py 3 dx 2 - y 2 doped holes enter the O-2 p orbitals and form Z-R singlets t-J-model: motion of holes in AF background

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 3 d 82 p 5 config. => metallic behavior e. g. La. Sr. Ni. O 4 • Ni+ : Rare! Needs planar coordination as in La. Ni. O 2

Differing Results in LDA + U La. Ni. O 2 Anisimov, Bukvalov & Rice PRB `99 get AFI similar to Ca. Cu. O 2 Lee & Pickett PRB `04 get weakly AFM unlike Ca. Cu. O 2 Expt. Hayward et al J. Am. Chem. insulator with Curie -Weiss S=1/2 & = - 257 K; 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 Site of Disorder Eisaki et al PRB 69, 064512 (`04) (a) Most Damage & (c) Least Damage Single Layer Bilayer Trilayer N. B. Cuprates with good surfaces are in (a) BSCCO & Na-CCOC Hg & Tl Cuprates

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

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

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

STM Patterns on Na-CCOC Kohsaka et al Science 315, 1380 `07 + Cu sites 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 4 a 0 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 Na-CCOC Y Chen, TMR & FCZhang PRL`07 STM tip couples to the outermost orbitals => 3 pz 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.

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 Underdoped Na-CCOC 1/4 of BZ M => Too Many Holes ( x= 0. 15 & 0. 2) — Yang, TMR & Zhang`06

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

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 ?

2 -Leg Ladder Compounds with Cu 2 O 3 - planes Sr. Cu 2 O 3 Sr 14 Cu 24 O 41 — Tel. No. Compound <— Cu. O 2 chains <— Cu 2 O 3 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 1 D 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. • there compounds with doped Cu 2 O 3 - planes similar to the many Are cuprates with doped Cu. O 2 planes and would this enhance Tc ?

Pattern Cu. O 2 with Zn. O 2 —> weakly coupled Cu. O 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 single groundstate of an island may be possible

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