t-J model for High-Tc Cuprates Superconductors

Kitaoka Lab. M1Yusuke Yanai

Wei-Qiang Chen et al., EPL, 98 (2012) 57005

Contentsintroduction

Introduction・ High-Tc Cuprate Superconductors (LSCO)

・ t-J Model

MotivationCalculation model ・ t-J Model for multilayer cuprates

Results ＆ Discussion ・ Calculation ・ Comparison between NMR Exp. and theory

Summary

La2-xSrxCuO4 　

(LSCO)

crystal structures of multilayered cuprates

La3+ Sr⇒ 2+

Sr

‐eHole dope

charge-reservoir layer

La2-x3+Srx

2+Cu(2+x)+O42-

High-Tc Cuprate Superconductorsintroduction

CuO2 plane

charge-reservoir layer

Experiment

La2CuO4

Cu2+

(3d9)

Antiferromagnetism(AFM)

ｔ≪Ｕ　⇒　Mott insulator

Cu O

t

Cu O

U

Cu O

t-J modelintroduction

x2-y2

3z2-r2

xy

yzzx

J∝t2/U

La2CuO4

Cu2+

(3d9)

La3+2-xSr2+

xCuO4

Cu2+x

Antiferromagnetism(AFM)

ｔ≪Ｕ　⇒　Mott insulator

Superconductivity(SC)

Cu O

t

Cu O

U

Cu O

t-J modelintroduction

x2-y2

3z2-r2

xy

yzzx

x2-y2

3z2-r2

xy

yzzx

Sr

t

Cu O

J∝t2/U

J∝t2/U

t-J model

AF+SC

t-J modelmotivation

due to disorder

multilayer

coexistSpin glassoverhang of AFM

t-J model

AF+SC

t-J modelmotivation

Sample Ba2Ca3Cu4O8(FyO1−y)2

similar

crystal structures of multilayered cuprates

t-J model

AF+SC

t-J modelmotivation

Sample Ba2Ca3Cu4O8(FyO1−y)2

only single-layerJ=0.3t Variational

Monte Carloon t-J modelMAFM

ΔSC

S. Pathak et al. 　 PRL 102, 027002 (2009) G. J. Chen et al., PRB 42, 2662 (1990).T. Giamarchi et al., PRB 43, 12 943(1991).A. Himeda and M. Ogata, PRB 60, R9935 (1999).

similar

Include interlayer coupling in t-J model.

T=0K ground state

SC gapMagnetic moment

t-J model for a single-layer

t : hopping integralJ : super exchange coupling

CuO

t J

t’

Charge Reservoir

Charge Reservoir

PG : Gutzwiller projection operatorc : an annihilation operator

PG = 10

t-J model for more than two layers

Charge Reservoir

Charge Reservoir

t⊥

J⊥

Cu O

t J

t’

Electrostatic energy in the unit cell

d

- - - - - - - - - -

- - - - - - - - - -

+ + +

+ + +

+ + + + + + +

+ + + + + + +

xi : hole concentration of IPxo : hole concentration of OPx : average hole concentration

x=(xi+xo)/2

Charge Reservoir

Charge Reservoir

CV2/2

Ees : electrostatic energyd : distance between two adjacent CuO2 layers

E×2S=ρS/εrε0

Gauss' law

E : electric fielda : lattice constantεr : relative dielectric 　 　 　 　 　 　 　 　 　constant

Sρ=ex/a2E

Total Hamiltonian

Calculation of Δ and mresult

εr=50

Experiments on multilayer can capture the essential physics of single-layer t-J model.

OPOPIP IPMag

netic

m

omen

t

Mag

netic

m

omen

t

εr=50

IP IP

OPOP

εr=200

SC g

ap

SC g

ap

single-layer results(dashed line)

single-layer results (dashed line)

SC gap is decided by single-layer property.

Magnetic moment is also decided by single-layer property.

SC gapMagnetic moment

εr=200

result

OPOPIP IPMag

netic

m

omen

t

Mag

netic

m

omen

t

SC g

ap

SC g

ap

single-layer results (dashed line)

Charge Reservoir

εr=200

Charge Reservoir

εr=50

Independent of εr

Total Hamiltonian

Calculation of Δ and m

IP IP

OPOP

εr=200 εr=50

single-layer results(dashed line)εr=200 εr=50

Comparison between NMR Exp. and theorydiscussion

yNMR Exp. Theory

xop mop xip mip εr mop mip

0.6 0.141 0 0.089 0

0.7 0.111 0 0.074 0.08

0.8 0.092 0 0.069 0.12

1 0.073 0.11 0.059 0.18

estimate

Charge Reservoir

Charge Reservoir

xop

xop

xip

xip

Sample Ba2Ca3Cu4O8(FyO1−y)2

under dope

over dope

Comparison between NMR Exp. and theorydiscussion

yNMR Exp. Theory

xop mop xip mip εr mop mip

0.6 0.141 0 0.089 0 87

0.7 0.111 0 0.074 0.08 107

0.8 0.092 0 0.069 0.12 170

1 0.073 0.11 0.059 0.18 247

estimate

Magnetic moment calculated by theory

Charge Reservoir

Charge Reservoir

xop

xop

xip

xip

Sample Ba2Ca3Cu4O8(FyO1−y)2

under dope

over dope

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.00

0.05

0.10

0.15

0.20

0.25

0.30

IP(NMR) IP(Theory)

m

p

yNMR Exp. Theory

xop mop xip mip εr mop mip

0.6 0.141 0 0.089 0 87 0.010 0.096

0.7 0.111 0 0.074 0.08 107 0.043 0.137

0.8 0.092 0 0.069 0.12 170 0.093 0.150

1 0.073 0.11 0.059 0.18 247 0.138 0.173

Comparison between NMR Exp. and theorydiscussion

Sample Ba2Ca3Cu4O8(FyO1−y)2

over dope

NMR

Theory

Mag

netic

m

omen

t

under dope

Large!!

yNMR Exp. Theory

xop mop xip mip εr mop mip

0.6 0.141 0 0.089 0 87 0.010 0.096

0.7 0.111 0 0.074 0.08 107 0.043 0.137

0.8 0.092 0 0.069 0.12 170 0.093 0.150

1 0.073 0.11 0.059 0.18 247 0.138 0.173

Comparison between NMR Exp. and theorydiscussion

εr=200 εr=50

IP IP

OPOP

xc (Theory) =0.2

xc (NMR) =0.16

Hidekazu Mukuda et al., J. Phys. Soc. Jpn. 81 (2012) 011008

0.8 time

Sample Ba2Ca3Cu4O8(FyO1−y)2

over dope

under dope

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.00

0.05

0.10

0.15

0.20

0.25

0.30

IP(NMR) IP(Theory) IP(Theory)

m

p

yNMR Exp. Theory

xop mop xip mip εr mop mip

0.6 0.141 0 0.089 0 87 0.010 0.096

0.7 0.111 0 0.074 0.08 107 0.043 0.137

0.8 0.092 0 0.069 0.12 170 0.093 0.150

1 0.073 0.11 0.059 0.18 247 0.138 0.173

Comparison between NMR Exp. and theorydiscussion

better agreement with experiment

Theory

NMRMag

netic

m

omen

t

Sample Ba2Ca3Cu4O8(FyO1−y)2

over dope

under dope

We consider 4-layer cuprates as t-J model including interlayer coupling.

Magnetic moment and SC gap are decided by single-layer property.

The result of theory is good agreement with that of experiment.

It is the future problem to pursue the compatibility of values calculated from experiments and theories.

Summary

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.00

0.05

0.10

0.15

0.20

0.25

0.30

IP(NMR) IP(Theory) IP(Theory)

mp

Theory

NMR

Thank you for your attention.