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

kitefleaUrban and Civil

Nov 15, 2013 (3 years and 10 months ago)

88 views

Presented by

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

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.

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

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

University

of Cincinnati

D. Scalapino

University

of California

Paul Kent

Thomas Maier

Thomas Schulthess

Oak Ridge

National Lab