Encounters with Oxides - Wins and Losses - Maurice Rice ETHZ & HKU

- A Look back to the Sixties

- New Physics in Oxides

- High-Tc Cuprate Oxides - The Big Surpise that continues

- Future Prospects

The CAT and the CREAM

I might remark that in low-temperature physics the disappearance of liquid helium, superconductivity, and magneto-resistance from the list of unsolved problems has left this branch of research looking pretty sick from the point of view of any young innocent who thinks he is going to break new ground.

A. B. Pippard Physics Today, 1961

The last generation of settlers in the new land of Physics found it green and fertile; we shall leave it a dustbowl.

Even number of electrons/unit cell

Band picture - electrons in momentum space

electrons in a periodic potential form Bloch waves and energy bands

Bloch waves

€

ϕn,r k (

r r )=ei

r k ⋅

r r un.

r k (

r r ) Energy eigenvalues

€

εn(r k )

Odd number of electrons/unit cell E

metal insulatorsemiconductor

E

energy gap

Repulsive interaction between electrons is a perturbation

Fermi sea

Fermi liquid of “independent”Quasiparticles (Landau, 1956)

Insulator, Semiconductor

Metal

Cooper Pairs of electrons formed by an attraction

Conventional Superconductivity

Conventional pairing

angular momentum l =0 spin singletBardeenCooperSchrieffer

‘57

Specific Heat C(T) vanishes exponentially as T ->0

Pairing Amplitude constant around Fermi Suface

Energy gap also constant

Macroscopic Coherent Pair Wavefunction forms for T<Tc : analagous to a Bose-Einstein Condensate of bosons

BCS Theory explains all features of conventional superconductors

Attractive interaction through electron-phonon interaction

Where did Pippard go wrong ?

Some Examples

- Semiconductors -> Artificially Structured Materials led to new devices & new physics e.g. Quantum Hall Effect

- Metals -> New Compounds led to new physics e.g. Oxides with strongly interacting electrons which

show new properties - Hi-Tc supeconductivity

V2O3 : First Example of a Mott Transition between a Metal and Localized Insulator without a symmetry change McWhan,Rice `69

Atomic limit - electrons localized in real space

Lattice of H-Atoms: aB << d

e-e - repulsion: U = E(H+) + E(H-)

Electrons localized: Mott Insulator

Low-energy physics purely dueto electron spins

€

HHeisenberg=Jr S i ⋅

r S j

i, j

∑

antiferromagnetic spin ordergenerally at low T

H+H-

H

2aB d

-t

S=1/2

STRONG

Fundamentally different from a band insulator

> 2zt

Metallic State shows Landau Fermi Liquid Behavior No Superconductivty alas! - just an enhanced effective mass m*

Brinkman - Rice Theory (1970)

The Fermi Surface of a metallic state disappears thru‘ a diverging m* as the Mott insulator is approached -> neglects J (AF Interactions)works beautifully in 3He ( Infinite U)

„ High- Tc“ Superconductivity in a oxide near

a Metal-Insulator Transition Sleight et al `75

Tc = 10K at x=0.3

Insulator is a CDW with Bi+3 & Bi+5 sites

melting of el. Pairs leads to Superconductivity - Rice&Sneddon `81 - Yoshioka-Fukuyama `85

Interpenetrating s.c. lattice of X and O ions XO (1D) , XO2 (2D) & XO3 (3D)

O2- - Ion Displacement Pattern in 2D is unfrustrated !

Result : A Charge Density Wave in BaBiO3

i.e. 2 Sublattices with Bi3+ & Bi5+ ions

leading to an energy gap in the Bi-6s band

G. Bednorz

&

K.A. Müller

(La/Ba)2CuO4 YBa2Cu3O7

C.W. Chu

&

M.K. Wu

MgB2

SuperconductivityTc over time

But we started from the wrong groundstate ! La2CuO4 is an Antiferromagnetic not a CDW Insulator

First Idea : The CuO2 -planes are similar to the BiO3 lattices

Doping a CDW insulator leads to a Superconductor but Tc is low !

Better Example: Ba1-xKxBaO3 Mattheiss et al,Cava et al, Hinks et al

`88

Reason is that CDW state is much more stable than AF state !

TcCDW =

EFe1/(TN=const. J

High Temperature Superconductivity

CuO2 plane

Copper-oxide compounds

1986: J.G. Bednorz & K.A. Müller

La2-xBaxCuO4 Tc =35 K

AFSC

T

x

TN

Tc

T*

Doped antiferromagneticMott insulator

under optimally overdoped

spin gap

strangemetal

Tc up to 133K Schilling & Ott ‘93

Are they unconventional superconductors? Not ordinary metals!

Generic Phase Diagram

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.^

Tc

Singlet Pairing of Cu2+-Spins in the Pseudogap Phase

Well Ordered and Underdoped

- Continuous Onset of Spin Pairing in Normal Phase- Spin Susceptibility well below AF value at T ~ Tc

- Hole Doped Insulator in Pseudogap Phase

YBa2Cu4O8

Knight Shift ~ Spin Susceptibility

Mali et al + . . .

New Powerful Experimental Tools : (Surface Sensitive)

• ARPES (Angle Resolved Photoemission Spectroscopy)• Measures A(k,) = Im G(k,) - Shen, Campuzano, Fink, Johnston

• STM (Scanning Tunneling Spectroscopy)• Measures local D.O.S. to add/remove an electron- Fischer, Davis

Phase Sensitive Experiments to determine symmetry

Symmetry of Cooper Pairs

Pair wavefunction:

€

Fss'(r k )=⟨ˆ c r k s

ˆ c −r k s'⟩=Φ(

r k )χ (s,s')

totally antisymmetric under electron exchange

'sskk ↔−→rr

even parity )()( kkrr

Φ=−Φ

)()( kkrr

Φ−=−Φodd parity

S=0 singlet

S=1 triplet

L = 0,2,4,...

L=1,3,5,…

orbital spin

Broken symmetries: U(1)-gauge symmetry Superconductivity Crystal deformation time reversal magnetism

Tsuei, Kirtley et al. (1995)

Tri-Crystal Geometry

Superconducting loop YBa2Cu3O7 Tc = 92 K = 60 m

Tsuei-Kirtley frustrated loops

SQUID-scanning-microscope measures the magnetic field that results from the current

frustrated loops lead toa current in groundstate

magnetic field

Odd number of -shifts

Basic model for doped cuprates

Single 2D Mott band lightly doped with holes

€

H = −t c is+ 1− ni,−s( ) 1− n j,−s( )c js + hc.{ }

i, j ,s

∑ + Jr S i ⋅

r S j

i, j

∑

Mobile Holes and Interacting Spins

t-J model: J/t = 1/3

Intrinsic strong coupling between hole motion and spin configuration makes it very difficult to analyse

Cu2+: S=1/2 Zhang-Rice Singlet Cu3+: S=0

2D RVB State which is a superposition of configurations with Singlet Pairs can be written as a projected BCS - State.

Explains many features of Hi-Tc

- Anderson et al J Phys C ‘04

singlet

Resonating Valence Bond Theory

Doping allows singlets to move

Proposed by Anderson ‘87

Singlet energy gain is 3x Classical energy

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

ARPES on Ca2Na2-xCuCl2O2 -Shen et al ‘05

Weight at Fermi energy

Extrapolated using minimum energy gap to obtain “Fermi surface”

“Fermi surface” violates Luttinger Sum Rule!- Electron doped !

shows only Fermi arcs

K. M. Shen et al., Science 307, 901 (2005)

pocket

“FS”

Comparison with ARPES experiments - Phenom. RVB Yang,Rice &Zhang ‘06

News & Views Nature 3 Aug 06

A.Cho Science 4 Aug 06

D.J.Scalapino Nature Physics News &Views Sept. `06

Examples of dI/dV spectra at various points on surface

Peaks in in these spectra at a roughly const. energy

Simliar to those observed in classic superconductors e.g. Pb ?

€

d2I /d2V

BSSCO Surface in BiO layer but statesat are in layer

-> els tunnel thru`apical O ion.

This can lead to emission of apical O-phonons.

Tunneling Path in space & in energy with emission of phonon

€

E f

€

CuO2

Pilgram,Rice & Sigrist `06

Note Multiphonon Peaks at larger values of El.-Phonon Coupling

Conclusions

Phonon Sidebands in STM can arise from inelastic tunneling thru‘ apical O

Spatial Anticorrelation between phonon energy and energy gap in STM spectra can arise from local variations in the structure of planes due to BiO superlattice, Bi:Sr nonstoichiometry etc

Case for an Electron-Phonon Mechanism for High-Tc is unproven !

But have we reached the end of the road for BCS superconductors?

€

CuO2

MgB2 - a 21stcentury high-temperature superconductor

Tc = 39 K

(Akimitsu et al. 2001)

2D -band dominant3D -band passive

Isoelectronic to GraphiteModerately strong el.-ph. coupling to B-B mode Mazin,Andersen,Pickett & - -

Fermi Surface(green) difficult to obtain.

Prediction of a High - Tc in a material with a band Fermi Surface

Rosner,Kitaigorodsky & Pickett `02

LiBC isoelectronic to MgB2

is a semiconductor

Can it be hole doped ? e.g. Li1-x BC

so far NO!

Future Prospects

New Materials are still being discovered

New Ideas on tailoring known materials may be a better way to go