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

2 Schulthess_Superconductivity_SC07

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

3 Schulthess_Superconductivity_SC07

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

4 Schulthess_Superconductivity_SC07

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

5 Schulthess_Superconductivity_SC07

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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6 Schulthess_Superconductivity_SC07

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

7 Schulthess_Superconductivity_SC07

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

++-

-

8 Schulthess_Superconductivity_SC07

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

9 Schulthess_Superconductivity_SC07

• 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).

10 Schulthess_Superconductivity_SC07

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?

11 Schulthess_Superconductivity_SC07

Contacts

Thomas Maier

Computational Materials Sciences

Computer Science and Mathematics Division

(865) 576-3597

maierta@ornl.gov

Paul Kent

Computational Materials Sciences

Computer Science and Mathematics Division

(865) 574-4845

kentpr@ornl.gov

Thomas Schulthess

Computational Materials Sciences

Computer Science and Mathematics Division

(865) 574-1942

schulthesstc@ornl.gov

11 Schulthess_Superconductivity_SC07

12 Schulthess_Superconductivity_SC07

The team

M. Jarrell

Universityof Cincinnati

D. Scalapino

Universityof California

Paul Kent

Thomas Maier

Thomas Schulthess

Oak RidgeNational Lab