Fermion Glue in the Hubbard Model: New Insights into the Cuprate Pairing Mechanism with Advanced Computing

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Nov 15, 2013 (3 years and 4 months ago)

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Fermion Glue in the Hubbard Model:

New Insights into the Cuprate Pairing
Mechanism with Advanced Computing

Thomas C. Schulthess

Computational Materials Sciences

Computer Science and Mathematics Division

2

Schulthess_Superconductivity_SC07

Superconductivity

A model for high
-
temperature

superconductors

Algorithm and

leadership computing

New scientific insights

t

t

U

Outline

0.0

2.5

3.0

2.0

1.5

1.0

0.5

50

40

30

20

10

0

-
10

-
20

-
30

T/t

U = 8t; N
o

= 4;(n) = 0.85

V
d

3/2

m

1/2

d


irr

Superconductor

Non
-
super
-

conductive metal

0 K

Tc

Temperature

Resistance

3

Schulthess_Superconductivity_SC07

What is superconductivity?


A macroscopic
quantum state with


Zero resistance


Perfect diamagnetism


Applications:


MAGLEV, MRI,

power transmission,
generators, motors


Only disadvantage:


Cooling necessary


T
c

≈ 150 K in HTSC


Ultimate goal:


T
c

≈ room temperature

Superconductor

Non
-
super
-

conductive metal

0 K

T
c

Temperature

Resistance

0

20

40

60

80

100

LHe

LH
2

LNe

LN
2

Power requirements

for cooling versus

temperature

in Kelvin

4

Schulthess_Superconductivity_SC07

Discovered by

Bednorz and Müller

in 1986


Highly anisotropic


Superconducting

CuO planes

High
-
temperature superconductors

Liquid

He

140

100

60

20

T [K]

1920

1960

1980

1940

2000

TIBaCaCuO 1988

HgBaCaCuO 1993

BiSrCaCuO 1980

La
2
-
x
Ba
x
CuO
4

1986

Nb=A1=Ge

Nb
3
Ge

MgB
2

2001

Nb
3
Su

NbN

Nb

Hg

Pb

NbC

V
3
Si

YBa
2
Cu
3
O
7

19870

High temperature

non
-
BCS

Low
temperature
BCS

Bednorz

and Müller

BCS Theory

Liquid H
2

HgTlBaCuO 1995

5

Schulthess_Superconductivity_SC07

HTSC: 10
23


interacting electrons

2
-
D Hubbard model

for CuO planes

DCA/QMC:

Map Hubbard model
onto embedded cluster

2
-
D Hubbard model of

high
-
temperature superconductors

t

t

U

6

Schulthess_Superconductivity_SC07

G

Warm up

Sample

QMC time



dger

or delay updating



dgemm

(N

=

4480
)

(
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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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.

95
, 237001 (2005).

Superconductivity as a
consequence of strong
electronic correlations

N
c

Z
d

T
c


4A

0

0.056


8A

1

-
0.006


12A

2

0.016


16B

2

0.015


16A

3

0.025


20A

4

0.022


24A

4

0.020


26A

4

0.023

+

+

-

-

QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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
.
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

-
30

0.0

2.5

3.0

2.0

1.5

1.0

0.5

T/t

U = 8t; N
o

= 4; (n) = 0.85

Spin

Charge

V
d

3/2

m

1/2

d


irr

+

+

-

-

Magnetic origin of pairing interaction

QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
9

Schulthess_Superconductivity_SC07


Test simple spin fluctuation representation

of pairing interaction and calculate T
c

in Hubbard model






Future: Demonstrate validity of Hubbard model
simulations


Measure spin susceptibility in neutron scattering experiments
and calculate T
c

Spin susceptibility representation

enables neutron scattering validation

<n>

0.95

0.90

0.85

T
c0

0.080

0.074

0.067

T
c0
(1)

0.100
(25%)

0.087

(18%)

0.074

(10%)

T
c0
(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).

10

Schulthess_Superconductivity_SC07

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?

11

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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

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The team

M. Jarrell

University

of Cincinnati

D. Scalapino

University

of California

Paul Kent

Thomas Maier

Thomas Schulthess

Oak Ridge

National Lab