1. Kitaoka Lab. M1 Yusuke Yanai Wei-Qiang Chen et al., EPL, 98 (2012) 57005

2. introduction  Introduction ・ High-Tc Cuprate Superconductors (LSCO) ・ t-J Model  Motivation  Calculation model ・ t-J Model for multilayer cuprates  Results ＆ Discussion ・ Calculation ・ Comparison between NMR Exp. and theory  Summary

3. La 2-x Sr x CuO 4 (LSCO) crystal structures of multilayered cuprates La 3+ ⇒ Sr 2+ Sr ‐e‐e ‐e‐e Hole dope charge- reservoir layer La 2-x 3+ Sr x 2+ Cu (2+x)+ O 4 2- High-T c Cuprate Superconductors introduction CuO 2 plane charge- reservoir layer Experiment

4. La 2 CuO 4 Cu 2+ (3d 9 ) Antiferromagnetism(AFM ) ｔ≪Ｕ ⇒ Mott insulator Cu O t O U O t-J model introduction x 2 -y 2 3z 2 -r 2 xy yz zx J ∝ t 2 /U

5. La 2 CuO 4 Cu 2+ (3d 9 ) La 3+ 2-x Sr 2+ x CuO 4 Cu 2+x Antiferromagnetism(AFM ) ｔ≪Ｕ ⇒ Mott insulator Superconductivity(SC) Cu O t O U O t-J model introduction x 2 -y 2 3z 2 -r 2 xy yz zx x 2 -y 2 3z 2 -r 2 xy yz zx Sr t Cu O J ∝ t 2 /U

6. t-J model AF+SC t-J model motivation due to disorder multilayer coexist Spin glass overhang of AFM

7. t-J model AF+SC t-J model motivation Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 similar crystal structures of multilayered cuprates

8. t-J model AF+SC t-J model motivation Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 only single-layer J=0.3t Variational Monte Carlo on t-J model M AFM Δ SC 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 gap Magnetic moment

9. t-J model AF+SC t-J model motivation due to disorder multilayer Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 Include interlayer coupling in t-J model. coexist Spin glass overhang of AFM similar only single-layer

10. t-J model motivation crystal structures of multilayered cuprates Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 S. Pathak et al. PRL 102, 027002 (2009) J=0.3t Variational Monte Carlo on t-J model M AFM Δ SC 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).) T=0K ground state 4-layer ？

11. t : hopping integral J : super exchange coupling Cu O t J t’ Charge Reservoir P G : Gutzwiller projection operator c : an annihilation operator P G = 10

12. Charge Reservoir t⊥t⊥ J⊥J⊥ Cu O t J t’

13. d - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + x i : hole concentration of IP x o : hole concentration of OP x : average hole concentration x =( x i + x o )/2 Charge Reservoir CV 2 / 2 E es : electrostatic energy d : distance between two adjacent CuO 2 layers E× 2 S=ρS/ε r ε 0 Gauss' law E : electric field a : lattice constant ε r : relative dielectric constant S ρ=ex/a 2 E

14. Total Hamiltonian result ε r =50 Experiments on multilayer can capture the essential physics of single-layer t-J model. OPOP OPOP IP Magnetic moment ε r =50 IP OPOP OPOP ε r =200 SC gap single-layer results(dashed line) SC gap is decided by single-layer property. Magnetic moment is also decided by single-layer property. SC gap Magnetic moment ε r =200

15. result OPOP OPOP IP Magnetic moment SC gap single-layer results (dashed line) Charge Reservoir ε r =200 Charge Reservoir ε r =50 Independent of ε r Total Hamiltonian IP OPOP OPOP ε r =200 ε r =50 single-layer results(dashed line) ε r =200 ε r =50

16. discussion y NMR Exp.Theory x op m op x ip m ip εrεr m op m ip 0.60.14100.0890 0.70.11100.0740.08 0.80.09200.0690.12 10.0730.110.0590.18 estimate Charge Reservoir x op x ip Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 under dope over dope

17. discussion y NMR Exp.Theory x op m op x ip m ip εrεr m op m ip 0.60.14100.089087 0.70.11100.0740.08107 0.80.09200.0690.12170 10.0730.110.0590.18247 estimate Magnetic moment calculated by theory Charge Reservoir x op x ip Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 under dope over dope

18. y NMR Exp.Theory x op m op x ip m ip εrεr m op m ip 0.60.14100.0890870.0100.096 0.70.11100.0740.081070.0430.137 0.80.09200.0690.121700.0930.150 10.0730.110.0590.182470.1380.173 discussion Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 over dope NMR Theory Magnetic moment under dope Large!!

19. y NMR Exp.Theory x op m op x ip m ip εrεr m op m ip 0.60.14100.0890870.0100.096 0.70.11100.0740.081070.0430.137 0.80.09200.0690.121700.0930.150 10.0730.110.0590.182470.1380.173 discussion ε r =200 ε r =50 IP OPOP OPOP x c (Theory) =0.2 x c (NMR) =0.16 Hidekazu Mukuda et al., J. Phys. Soc. Jpn. 81 (2012) 011008 0.8 time Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 over dope under dope

20. y NMR Exp.Theory x op m op x ip m ip εrεr m op m ip 0.60.14100.0890870.0100.096 0.70.11100.0740.081070.0430.137 0.80.09200.0690.121700.0930.150 10.0730.110.0590.182470.1380.173 discussion better agreement with experiment Theory NMR Magnetic moment Sample Ba 2 Ca 3 Cu 4 O 8 (F y O 1−y ) 2 over dope under dope

21. 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. Theory NMR