fermion glue in the hubbard model: new insights into the cuprate … · 2007. 10. 31. ·...
TRANSCRIPT
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Presented by
Fermion Glue in the Hubbard Model:New Insights into the Cuprate PairingMechanism with Advanced Computing
Thomas C. Schulthess
Computational Materials Sciences
Computer Science and Mathematics Division
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SuperconductivitySuperconductivity A model for high-temperatureA model for high-temperaturesuperconductorssuperconductors
Algorithm andAlgorithm andleadership computingleadership computing
New scientific insightsNew scientific insights
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Outline
0.0 2.5 3.02.01.51.00.5
50
40
30
20
10
0
-10
-20
-30T/t
U = 8t; No = 4;(n) = 0.85
Vd
3/2 m
1/2 d
irr
Superconductor
Non-super-conductive metal
0 K Tc Temperature
Res
ista
nce
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What is superconductivity?
• A macroscopic quantumstate with
Zero resistance
Perfect diamagnetism
• Applications:
MAGLEV, MRI,power transmission,generators, motors
• Only disadvantage:
Cooling necessary
Tc 150 K in HTSC
• Ultimate goal:
Tc room temperature
Superconductor
Non-super-conductive metal
0 K Tc Temperature
Res
ista
nce
0 20 40 60 80 100
LHe
LH2
LNeLN2
Power requirementsfor cooling versus
temperaturein Kelvin
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Discovered byBednorz and Müllerin 1986
• Highly anisotropic
• SuperconductingCuO planes
High-temperature superconductors
LiquidHe
140
100
60
20
T [K
]
1920 1960 19801940 2000
TIBaCaCuO 1988
HgBaCaCuO 1993
BiSrCaCuO 1980
La2-xBaxCuO4 1986
Nb=A1=Ge
Nb3Ge
MgB2 2001
Nb3SuNbN
NbHg
Pb
NbC
V3Si
YBa2Cu3O7 19870
High temperaturenon-BCS
LowtemperatureBCS
Bednorz
and Müller
BCS Theory
Liquid H2
HgTlBaCuO 1995
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HTSC: 1023
interacting electrons2-D Hubbard model
for CuO planes
DCA/QMC:Map Hubbard model onto
embedded cluster
2-D Hubbard model ofhigh-temperature superconductors
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G
Warm upWarm up Sample QMC time
dger
or delay updating dgemm
(N = 4480)(N = 4480)
(4480 x 32)(4480 x 32)
Measurement cgemm
Warm up
G G
Warm up
G
Warm up
Algorithm and leadership computing:Fixed startup cost favors fewer,faster processors Cray X1E
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T. A. Maier, M. Jarrell, T. C. Schulthess, P. R. C. Kent, J. B. White,
Systematic study of D-wave superconductivity in the 2D repulsive Hubbard model,
Phys. Rev. Lett. 995, 237001 (2005).
Superconductivity as aconsequence of strongelectronic correlations
0.0234 26A
0.0204 24A
0.0224 20A
0.0250.02533 16A 16A
0.0150.01522 16B 16B
0.0160.01622 12A 12A
-0.006-0.00611 8A 8A
0.0560.05600 4A4A
TTccZZddNNcc
++-
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T. A. Maier, M. S. Jarrell, and D. J. Scalapino, Structure of the pairing
interaction in the two-dimensional Hubbard Model, Phys. Rev. Lett. 996,047005 (2006).
T. A. Maier, M. Jarrell, and D. J. Scalapino, Pairing interaction in the two-
dimensional Hubbard model studied with a dynamic cluster quantum Monte
Carlo approximation, Phys. Rev. B, 774, 094513 (2006).
T. A. Maier, M. Jarrell, and D. J. Scalapino, Spin susceptibility
representation of the pairing interaction for the two-dimensional Hubbard
model, Phys. Rev. B, 775, 134519 (2007).
• Attractive pairing interactionbetween nearest neighbor singlets
• Dynamics associated withantiferromagnetic spin fluctuation spectrum
• Pairing interaction mediated byantiferromagnetic fluctuations
Pairing
Fully irr.
50
40
30
20
10
0
-10
-20
-300.0 2.5 3.02.01.51.00.5
T/t
U = 8t; No = 4; (n) = 0.85
Spin
Charge
Vd
3/2 m
1/2 d
irr
++-
-Magnetic origin of pairing interaction
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• Test simple spin fluctuation representationof pairing interaction and calculate Tcin Hubbard model
• Future: Demonstrate validity of Hubbard model simulations
Measure spin susceptibility in neutron scattering experiments andcalculate Tc
Spin susceptibility representationenables neutron scattering validation
0.95 0.90 0.85
Tc0 0.080 0.074 0.067
Tc0(1)0.100(25%)
0.087(18%)
0.074(10%)
Tc0(2)0.108(35%)
0.084(14%)
0.064(4%)
“Exact” QMC
fitted from pairing interaction
fitted from single-particle spectrum
Electron filling
T. A. Maier, A. Macridin, M. Jarrell and
D. J. Scalapino, Systematic analysis of
a spin susceptibility representation of
the pairing interaction in the 2D Hubbard
Model, Phys. Rev. B, in press (2007).
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Summary/conclusions/outlook
• Superconductivity: A macroscopic quantum effect
• 2-D Hubbard model for strongly correlatedhigh-temperature superconducting cuprates
• Dynamic cluster quantum Monte Carlo simulationson Cray X1E
• Superconductivity as a result of strong correlations
• Pairing mediated by antiferromagnetic spin fluctuations
• Simple spin susceptibility representationof pairing interaction
• Verification by neutron scattering experiments?
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Contacts
Thomas Maier
Computational Materials Sciences
Computer Science and Mathematics Division
(865) 576-3597
Paul Kent
Computational Materials Sciences
Computer Science and Mathematics Division
(865) 574-4845
Thomas Schulthess
Computational Materials Sciences
Computer Science and Mathematics Division
(865) 574-1942
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The team
M. Jarrell
Universityof Cincinnati
D. Scalapino
Universityof California
Paul Kent
Thomas Maier
Thomas Schulthess
Oak RidgeNational Lab