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ANL-MSD BCS@50, UIUC, Oct. 11, 2007
High Temperature Superconductivity -After 20 years, where are we at?
Michael NormanMaterials Science Division
Argonne National Laboratory
Norman and Pepin, Rep. Prog. Phys. (2003)Norman, Pines, and Kallin, Adv. Phys. (2005)
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It All Started Back in 1986
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Tc Shot Up Like a Rock(many cuprates superconduct above 77K)
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May 11, 1987
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The Path to a Microscopic Theory was Littered with Many Famous Physicists
Einstein
Landau
Heisenberg
Feynman
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Eventually, Some Guys in Illinois Got It Right(Bardeen, Cooper, Schrieffer - 1956,1957)
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From Steve Girvin’s lecture (Boulder Summer School 2000) courtesy of Matthew Fisher
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e-
e-
(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)
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But cuprates haved-wave pairs!(L=2, S=0)
van Harlingen;Tsuei & Kirtley -Buckley Prize -1998
Artwork byGerald Zeldin (2000)
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Alexei 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)
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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
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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-Tcsuperconductivity does not exist.”
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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
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Why is the High Tc Problem So Hard to Solve?(Laughlin’s Lecture for Teachers - KITP, 2000)
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LaO
LaO
CuO2
Cu Cu
Cu Cu
!d
!p
AB
B
UHB
LHB
other
µ
Electronic Structure of Cuprates
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Cu2+Large U charge-transfer
gap Δpd ~ 2 eV
Mott insulatormetal?
doping
t = 0.3 eV, U = 2 eV, J = 4t2/U = 0.12 eV
J~1400 K
bestevidencefor large Uantiferromagnet
! ! "#
++$=
%%%
,, ji iiiji nnUcctH Hubbard
Short tutorial on cuprates
(slide from PWA/NPO)
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0
50
100
150
200
250
300
350
0 0.05 0.1 0.15 0.2 0.25 0.3
Tem
per
atu
re (
Kel
vin
)
Hole Doping (x)
superconductor
pseudogap
An
tife
rrom
agn
et
spinglass
"normal" state
FermiLiquid
T*
Tc
TN
Tcoh
(?)
Phase Diagram of Cuprates
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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 byphase sensitive tunneling -
van Harlingen, Kirtley & TsueiKirtley et al, Nat. Phys. (2006)
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Extraction of the Superconducting Energy Gap from PhotoemissionDing et al., PRL (1995) & PRB (1996)
Δk --> cos(kx) - cos(ky) --> Implies pair interaction peaked for near-neighbors
EM
M!
Y
1
15
Bi2212, Tc=87K
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00.040.080.12
Inte
nsi
ty
Binding energy (eV)
Photoemission spectrum above and below Tc at momentum k=(π,0) for Bi2212
Norman et al, PRL (1997)
peak
dip
Incoherent normal state
Coherent superconductor
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Neutron Spin Resonance below Tc (S=1 excitation)Rossat-Mignod/Bourges, Mook/Dai, Keimer/Fong
Dai et al, Nature (1999)
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Dispersion of magnetic excitations has the form of an hourglassArai et al, PRL (1999)
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The “strange metal” phase exhibits linear T resistivity
Martin et alPRB (1990)
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What is the Pseudogap?
1. Pre-formed pairs
2. Spin density wave
3. Charge density wave
4. d density wave
5. Orbital currents
6. Flux phase
7. Stripes
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Norman et al., Nature (1998)
T < Tc
Tc < T < T*
T > T*
Temperature evolution of the Fermi surface
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Evolution of the Fermi surface with doping
Doiron-Leyraud et alNature (2007)
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Is the T=0 limit of the pseudogap phase a nodal metal?
Kanigel et alNat. Phys. (2006)
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A Nernst signal (due to fluctuating vortices?) appears above Tc
Wang et alPRB (2001)
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Circular dichroism above Tc in the pseudogap phase?
Kaminski et alNature (2002)
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Orbital moments above Tc in the pseudogap phase?
Fauque et alPRL (2006)
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Scanning tunneling spectra show strong spatial inhomogeneity
McElroy et al, PRL (2005)
“gap map”
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Hole Density shows a “4a period bond centered electronic glass”
Kohsaka et al, Science (2007)
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Science, February 1987
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RVB has its critics
Bob LaughlinAnnals of Improbable Research, May-June 2004
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Neel Lattice RVB
RVB (“resonating valence bond”) is a strongcoupling theory for cuprates developed by Phil
Anderson and his colleagues
It postulates a liquid of spin singlets
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+ +
+ +
-
-
-
-
0
0.1
0.2
0.3
0 0.1 0.2 0.3x
!
!SC
The pseudogap phase corresponds to a d-wave pairing of spins(left panel). At zero doping, this is quantum mechanicallyequivalent to an orbital current phase (middle panel). The spingap, Δ, is not equivalent to the superconducting order parameter,Δsc, as it would be in BCS theory (right panel).
RVB Model (Anderson-Baskaran - 1987, Kotliar - 1988, Gros-Rice-Zhang, Lee-Nagaosa-Wen, Randeria-Trivedi, etc.)
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Two Theories of the Phase Diagram
Relation of T* to Tc
RVB Quantum Critical
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“Emery-Kivelson” picture Nature (1995)
T
x
superconductor
TMF
Tphase
pairing coherence
Pairing occurs below mean field transition temperatureCoherence occurs below phase ordering temperatureSuperconductivity occurs only below both temperatures
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SO(5) vs SU(2)
Demler, Hanke, and Zhang Lee, Nagaosa, and Wen Rev Mod Phys (2004) Rev Mod Phys (2006)
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-! 0 !
Veff (
qx,!
)
qx - !
0
Veff (
x,0
)
x
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
(plots from DJS)
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Dynamical Mean Field Theory (Georges, Kotliar, Tremblay)Magnetic correlations wipe out parts of the Fermi surface
Senechal & TremblayPRL (2004)
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McElroy - Nat. Phys. (2006)
Does charge ordering wipe out part of the Fermi surface?
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Kaminski et al, PRL (2001)
The dispersion kink at the node continuously evolves into a two branch dispersion (peak-dip-hump) as one approaches the anti-node
Spin resonance mode?
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Lanzara et al, Nature (2001)
The kink is seen in a variety of the cuprates at the same energyA phonon?
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d-wave pairing due to a half-breathing phonon mode??Shen, Lanzara, Ishihara, Nagaosa - Phil Mag B (2002)