High Temperature Superconductivity -After 25 years, where are we at?

Michael Norman

Materials Science DivisionArgonne National Laboratory

Norman, Science 332, 196 (2011)

Fermilab - June 22, 2011

It All Started Back in 1986

Tc Shot Up Like a Rock(many cuprates superconduct above 77K)

Woodstock of Physics - March 1987

H. K. Onnes (1911)

Zero resistance

Meissner effect (1933)

Superconductors:(1) They are perfect conductors(2) They expel magnetic flux

The Path to a Microscopic Theory was Littered with Many Famous Physicists

Einstein

Landau

Heisenberg

Feynman

Eventually, Three Guys in Illinois Got It Right(Bardeen, Cooper, Schrieffer - 1956,1957)

1. London theory - rigidity to macroscopic perturbations implies a “condensate” (1935,1950)

2. Ginzburg-Landau () theory - order parameter for condensate (1950)

3. Isotope effect (Maxwell, Serin & Reynolds, Frohlich, 1950)4. Cooper pairs (1956)5. Bardeen-Cooper-Schrieffer (BCS) microscopic theory (1957)6. Type-II superconductors (Abrikosov vortices, 1957)7. Connection of BCS to Ginzburg-Landau (Gorkov, 1958)8. Strong coupling superconductivity (Eliashberg, Nambu,

Anderson, Schrieffer, Wilkins, Scalapino …, 1960-1963)9. p-wave superfluidity in 3He (Osheroff, Richardson, Lee, 1972;

Leggett, 1972)10. Heavy Fermion Superconductivity (Steglich, 1979)11. High Temperature Superconductivity (Bednorz & Muller, 1986)12. Iron Arsenides (Hosono, 2008)

A (Very) Short History of Superconductivity

From Steve Girvin’s lecture (Boulder Summer School 2000) courtesy of Matthew Fisher

(the electron-phonon case)

1. 1st e- attracts + ions2. Ions shift position from red to blue3. 1st e- moves away4. 2nd e- sees + ion hole and moves to former position of 1st e-

Interaction is local in space(s-wave pairs, L=0, S=0)but retarded in time(Tc << Debye frequency)

Everything You Wanted to Know About Pair Formation(But Were Afraid to Ask)

But cuprates haved-wave pairs!(L=2, S=0)

van Harlingen;Tsuei & Kirtley -Buckley Prize -1998

Artwork byGerald Zeldin (2000)

Alex Abrikosov(small q phonons)

Bob Laughlin(competing phases)

Phil Anderson(RVB; interlayer tunneling; RVB)

Karl Mueller(bipolarons)

Bob Schrieffer(spin bags)

Tony Leggett(interlayer Coulomb)

1. Resonating valence bonds2. Spin fluctuations3. Stripes4. Anisotropic phonons5. Bipolarons6. Excitons7. Kinetic Energy lowering8. d-density wave9. Charge fluctuations10.Flux phases11.Gossamer superconductivity12.Spin bags13.SO(5)14.BCS/BEC crossover15.Plasmons16.Spin liquids

Not to Mention

Interlayer tunneling

Marginal Fermi liquid

van Hove singularities

Quantum critical points

Anyon superconductivity

Slave bosons

Dynamical mean field theory

Theories Connected with High Tc Superconductivity

Famous Books

Abrikosov - Nobel Lecture - Dec. 2003

Famous Quotes

“On this basis I was able to explain most of the experimental data about layered cuprates . . .

As a result I can state thatthe so called “mystery” of high-Tc

superconductivity does not exist.”

Ten Weeks of High Tc (to the tune of Twelve Days of Christmas)

On the first week of the program Friend Philip said to me All simply RVB (All sim-pl-ee R-r V B)

On the second week of the program Friend Douglas said to me Pair in a d-wave All simply RVB

On the third week of the program Friend David said to me It's magnons Pair in a d-wave All simply RVB

On the fourth week of the program Friend Chandra said to me Four current rings (fo-or current rings) It's magnons Pair in a d-wave All simply RVB

At the end of the program Friend Philip said to me Big Tent is stretching Visons escaping Visons are gapping Slave spinons pairing T sym-try breaking Stripes fluctuating S - O - 5 Four current rings It's magnons Pair in a d-wave All simply RVB    

--Ilya Gruzberg Smitha Vishveshwara Ilya Vekhter Aditi Mitra Senthil Matthew Fisher - -

KITP Web SiteHigh Tc Program - Fall 2000

Why is the High Tc Problem So Hard to Solve?(Laughlin’s Lecture for Teachers - ITP, 2000)

Electronic Structure of Cuprates

Len MattheissPRL (1987)

Energy vs Momentum

Fermi surface

Electronic structure from density functional theory

Cu2+Large U

charge-transfer gap pd ~ 2 eV

Mott insulatormetal?

doping

t = 0.3 eV, U = 2 eV, J = 4t2/U = 0.12 eV

J~1400 K

best evidence for large Uantiferromagnet

Hubbard

Short (and biased!) tutorial on cuprates

(slide from Phil Anderson)

Phase Diagram of Cuprates

1. There are 2e- pairs2. The pairs are d-wave (L=2, S=0)3. There are “normal” (i.e., 2e-) vortices4. Quasiparticles exist (but only below Tc)

What We DO Know

d-wave pairing observed by phase sensitive tunneling -

van Harlingen, Kirtley & TsueiKirtley et al, Nat. Phys. (2006)

Extraction of the Superconducting Energy Gap from Photoemission

Campuzano, Shen, Johnson – Buckley Prize (2011)

k --> cos(kxa) - cos(kya) --> Implies near-neighbor pairs

Bi2212, Tc=87K

Dirac cone Ding et al., PRB (1996)

Photoemission spectrum above and below Tc at momentum k=(,0) for Bi2212

Norman et al, PRL (1997)

peak

dip

Incoherent normal state

Coherent superconductor

Neutron Spin Resonance (S=1 excitation)Rossat-Mignod/Bourges, Mook/Dai, Keimer/Fong

Dai et al, Nature (1999)

Dispersion of magnetic excitations has the form of an hourglassArai et al, PRL (1999)

The “strange metal” phase exhibits linear T resistivity

Martin et alPRB (1990)

1. Spin singlets

2. Pre-formed pairs

3. Spin density wave

4. Charge density wave

5. d density wave

What is the Pseudogap Due to?

6. Orbital currents

7. Flux phase

8. Stripes/nematic

9. Valence bond solid/glass

10. Combination?

Norman et al., Nature (1998)

T < Tc

(node)

Tc < T < T*(Fermi arc)

T > T*(full FS)

Temperature evolution of the Fermi surface

Is the T=0 limit of the pseudogap phase a nodal metal?

Kanigel et al, Nat Phys (2006)Chatterjee et al, Nat Phys (2010)

A Nernst signal (due to fluctuating vortices?) appears above Tc

Wang et alPRB (2001)

Evolution of the Fermi surface with doping

Doiron-Leyraud et alNature (2007)

The Hall number is negative!

Doiron-Leyraud et al.Nature (2007)

LeBoeuf et al.,Nature (2007) and PRB (2011)

RH < 0 forms a dome around 1/8

electron pockets due to magnetic stripes?

Antiphase Stripes - Tranquada et al. - Nature (1995)Charge peaks at (±2x,0), Spin peaks at (1/2±x,1/2), x~1/8

spinpeaks

chargepeaks

dopedholes

localspins

Circular dichroism above Tc in the pseudogap phase?

Kaminski et alNature (2002)

Orbital moments above Tc in the pseudogap phase?

Fauque et alPRL (2006)

Science, February 1987

RVB has many critics

Bob LaughlinAnnals of Improbable Research, May-June 2004

Neel Lattice RVB

RVB (“resonating valence bond”) is a ‘strong coupling’ theory for cuprates developed by Phil

Anderson and his colleagues

It postulates a liquid of spin singlets

The pseudogap phase corresponds to a d-wave pairing of spins (left). At zero doping, this is quantum mechanically equivalent to an orbital current phase (middle). The spin gap, , is not equivalent to the superconducting order parameter, sc, as it would be in BCS theory (right).

RVB Model (Phil Anderson - 1987, Gabe Kotliar - 1988, Patrick Lee, Mohit Randeria, Maurice Rice, etc.)

Two Theories of the Phase Diagram

Relation of T* to Tc

RVB Quantum Critical

Chatterjee et al., PNAS (2011)

“Emery-Kivelson” picture Nature (1995)

Pairing occurs below mean field transition temperatureCoherence occurs below phase ordering temperatureSuperconductivity occurs only below both temperatures

SO(5) vs SU(2)

Demler, Hanke, and Zhang Lee, Nagaosa, and Wen Rev Mod Phys (2004) Rev Mod Phys (2006)

Antiferromagnetic spin fluctuations can lead to d-wave pairs(an e- with up spin wants its neighbors to have down spins)

Heavy Fermions - Varma (1986), Scalapino (1986)High Tc - Scalapino (1987), Pines (1991)

< Repulsive

< Attractive

d-wave pairing due to a half-breathing phonon mode?Shen, Lanzara, Ishihara, Nagaosa - Phil Mag B (2002)

Hartnoll, Science (2008)

Holographic approach to high temperature superconductors?