After 25 years, where are we at?

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High Temperature Superconductivity
-

After 25 years, where are we at?

Michael Norman


Materials Science Division

Argonne National Laboratory

Norman, Science 332, 196 (2011)

Fermilab

-

June 22, 2011

It All Started Back in 1986

T
c

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

(
Y
⤠瑨敯e礠
-

潲o敲e灡p慭整敲e景爠捯湤敮r慴攠
(
ㄹ㔰
)


䥳潴潰攠敦晥捴

M慸睥汬Ⱐ卥物渠☠&敹湯汤猬 䙲潨汩捨

ㄹ㔰
)


䍯潰敲

灡楲猠(
ㄹ㔶
)


䉡牤敥B
-
䍯潰敲
-
卣桲i敦晥r

(
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
3
He (
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

e
-
e
-
(the electron
-
phonon case)


1.
1st
e
-

attracts +
ions

2.
Ions shift position from
red

to
blue

3.
1st
e
-

moves away

4.
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

(
T
c

<< Debye frequency
)

Everything You Wanted to Know About Pair Formation

(But Were Afraid to Ask)

But cuprates have

d
-
wave pairs!

(
L=2, S=0
)


van Harlingen;

Tsuei & Kirtley
-

Buckley Prize
-
1998


Artwork by

Gerald 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 bonds

2.
Spin fluctuations

3.
Stripes

4.
Anisotropic phonons

5.
Bipolarons

6.
Excitons

7.
Kinetic Energy lowering

8.
d
-
density wave

9.
Charge fluctuations

10.
Flux phases

11.
Gossamer superconductivity

12.
Spin bags

13.
SO(5)

14.
BCS/BEC crossover

15.
Plasmons

16.
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 T
c

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 that

the so called

mystery


of high
-
T
c

superconductivity does not exist.


Ten Weeks of High T
c


(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 Site

High T
c

Program
-

Fall 2000

Why is the High T
c

Problem So Hard to Solve?

(Laughlin

s Lecture for Teachers
-

ITP, 2000)

LaO
LaO
CuO
2
Cu
Cu
Cu
Cu

d

p
AB
B
UHB
LHB
ot
he
r

Electronic Structure of Cuprates

Len Mattheiss

PRL (1987)

Energy vs Momentum

Fermi surface

Electronic structure from density functional theory

Cu
2+

Large U

charge
-
transfer

gap
D
pd
~ 2 eV

Mott insulator

metal?

doping

t

= 0.3 eV,
U

= 2 eV,
J

= 4
t
2
/
U

= 0.12 eV

J~1400 K

best
evidence


for large U

antiferromagnet












,
,
j
i
i
i
i
j
i
n
n
U
c
c
t
H
Hubbard

Short (and biased!) tutorial on
cuprates

(slide from Phil Anderson)

Phase Diagram of Cuprates

1.
There are 2e
-

pairs

2.
The pairs are d
-
wave (L=2, S=0)

3.
There are

normal


(i.e., 2e
-
) vortices

4.
Quasiparticles exist (but only below T
c
)

What We DO Know

d
-
wave pairing observed by
phase sensitive tunneling
-


van Harlingen, Kirtley & Tsuei

Kirtley
et al
, Nat. Phys. (2006)


Extraction of the Superconducting Energy Gap from Photoemission


Campuzano, Shen, Johnson


Buckley Prize (2011)


D
k

--
> cos(k
x
a)
-

cos(k
y
a)
--
> Implies near
-
neighbor pairs

0
10
20
30
0
20
40
60
80
F
S
a
n
g
le
1
15
|

|

(
m
e
V
)
Bi2212,
T
c
=87K

Dirac cone

Ding
et al.
, PRB (1996)

0
0.04
0.08
0.12
I
n
t
e
n
s
i
t
y
Binding energy (eV)
Photoemission spectrum
above

and
below

T
c


at momentum k=(
p
,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 hourglass

Arai
et al
, PRL (1999)

The

strange metal


phase exhibits linear T resistivity

Martin
et al

PRB (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 <
T
c

(node)

T
c

< 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 T
c

Wang
et al

PRB (2001)

Evolution of the Fermi surface with doping

Doiron
-
Leyraud
et al

Nature (2007)

The Hall number is negative!

Doiron
-
Leyraud
et al.

Nature (2007)

LeBoeuf

et al.
,

Nature (2007) and PRB (2011)

R
H

< 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

spin

peaks

charge

peaks

doped

holes

local

spins

Circular dichroism above T
c

in the pseudogap phase?

Kaminski
et al

Nature (2002)

Orbital moments above T
c

in the pseudogap phase?

Fauque
et al

PRL (2006)

Science, February 1987

RVB has many critics



Bob Laughlin

Annals 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,
D
, is not equivalent to
the superconducting order parameter,
D
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 T
c

RVB

Quantum Critical

Chatterjee

et al.,

PNAS (2011)


Emery
-
Kivelson


picture


Nature (1995)

T
x
s
upe
rc
onduc
t
or
T
MF
T
pha
s
e
pa
i
ri
ng
c
ohe
re
nc
e
Pairing occurs below mean field transition temperature

Coherence occurs below phase ordering temperature

Superconductivity 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 T
c

-

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?

CU Physics Department Colloquium
CU Physics Department Colloquium
Monday, April 25, 2011 4:10 PM 428 Pupin Hall
Monday, April 25, 2011 4:10 PM 428 Pupin Hall
AdS/CFT is a conjectured duality between weak
coupling gravity in anti de Sitter space and a
strong coupling field theory on the boundary of
this space.
It has been suggested that a variety of
phenomena in condensed matter physics might be
explained by this approach. We will take a serious
look at several of these, including the presence of
Fermi arcs in the pseudogap
phase, the peak-dip-
hump lineshape
in the superconducting state, and
the origin of cuprate
s
uperconductivity.
In all of
these cases, I will argue that AdS/CFT has not
shed much light, nor is likely to, on the basic
issues being debated.
Micha el Nor ma n, Ar gonne Na t iona l La bor a t or y
Micha el Nor ma n, Ar gonne Na t iona l La bor a t or y