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Fermion Glue in the Hubbard Model:New Insights into the Cuprate Pairing Mechanism with Advanced Computing
Thomas C. SchulthessComputational 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
3/2m
1/2d
irr
Superconductor
Non-super-conductive metal
0 K Tc Temperature
Resi
stan
ce
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What is superconductivity? A macroscopic
quantum state 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
Resi
stan
ce
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 Superconducting
CuO planes
High-temperature superconductors
LiquidHe
140
100
60
20
T [K
]
1920 1960 19801940 2000
TIBaCaCuO 1988
HgBaCaCuO 1993
BiSrCaCuO 1980
La2-xBaxCuO4 1986Nb=A1=Ge
Nb3Ge
MgB2 2001
Nb3SuNbNNb
Hg
PbNbC
V3Si
YBa2Cu3O7 19870
High temperaturenon-BCS
Low temperature BCS
Bednorzand Müller
BCS Theory
Liquid H2
HgTlBaCuO 1995
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HTSC: 1023 interacting electrons 2-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
➙ dgeror 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. 95, 237001 (2005).
Superconductivity as a consequence of strong electronic correlations
NNcc ZZdd TTcc
4A4A 00 0.0560.056 8A8A 11 -0.006-0.006
12A12A 22 0.0160.016 16B16B 22 0.0150.015 16A16A 33 0.0250.025 20A 4 0.022 24A 4 0.020 26A 4 0.023
++-
-
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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. 96, 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, 74, 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, 75, 134519 (2007).
Attractive pairing interaction between nearest neighbor singlets
Dynamics associated with antiferromagnetic spin fluctuation spectrum
Pairing interaction mediated by antiferromagnetic 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
3/2m
1/2d
irr
++-
-Magnetic origin of pairing interaction
QuickTime™ and aTIFF (Uncompressed) decompressor
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QuickTime™ and aTIFF (Uncompressed) decompressor
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QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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Test simple spin fluctuation representationof pairing interaction and calculate Tc in Hubbard model
Future: Demonstrate validity of Hubbard model simulations Measure spin susceptibility in neutron scattering experiments
and calculate Tc
Spin susceptibility representationenables neutron scattering validation
<n> 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
Ū fitted from pairing interaction
Ū 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 correlated
high-temperature superconducting cuprates Dynamic cluster quantum Monte Carlo simulations
on Cray X1E Superconductivity as a result of strong correlations Pairing mediated by antiferromagnetic spin fluctuations Simple spin susceptibility representation
of pairing interaction Verification by neutron scattering experiments?
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Contacts
Thomas MaierComputational Materials SciencesComputer Science and Mathematics Division(865) [email protected]
Paul KentComputational Materials SciencesComputer Science and Mathematics Division(865) [email protected]
Thomas SchulthessComputational Materials SciencesComputer Science and Mathematics Division(865) [email protected]
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The team
M. Jarrell
Universityof
CincinnatiD. Scalapino
Universityof
CaliforniaPaul Kent
Thomas MaierThomas Schulthess
Oak RidgeNational Lab
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