Presented by

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

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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

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QuickTime™ and aTIFF (Uncompressed) decompressor

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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) 576-3597maierta@ornl.gov

Paul KentComputational Materials SciencesComputer Science and Mathematics Division(865) 574-4845kentpr@ornl.gov

Thomas SchulthessComputational Materials SciencesComputer Science and Mathematics Division(865) 574-1942schulthesstc@ornl.gov

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The team

M. Jarrell

Universityof

CincinnatiD. Scalapino

Universityof

CaliforniaPaul Kent

Thomas MaierThomas Schulthess

Oak RidgeNational Lab