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t-J model for High- T c Cuprates Superconductors

t-J model for High- T c Cuprates Superconductors. Wei- Qiang Chen et al ., EPL , 98 (2012) 57005. Kitaoka Lab. M1 Y usuke Yanai. introduction. Contents. Introduction ・ High- Tc Cuprate Superconductors (LSCO) ・ t-J Model Motivation Calculation model

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t-J model for High- T c Cuprates Superconductors

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  1. t-J model for High-TcCuprates Superconductors Wei-Qiang Chenet al., EPL, 98 (2012) 57005 Kitaoka Lab. M1 Yusuke Yanai

  2. introduction Contents • Introduction・ High-TcCuprate 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. introduction High-TcCuprate Superconductors La3+⇒ Sr2+ La2-x3+Srx2+Cu(2+x)+O42- charge-reservoir layer crystal structuresof multilayered cuprates Hole dope Experiment ‐e Sr CuO2 plane charge-reservoir layer La2-xSrxCuO4(LSCO)

  4. introduction Cu O t-J model La2CuO4 Cu2+ x2-y2 (3d9) 3z2-r2 xy yz zx Cu Cu O O t J∝t2/U U Antiferromagnetism(AFM) ｔ≪Ｕ　⇒　Mott insulator

  5. introduction Cu O t-J model La3+2-xSr2+xCuO4 La2CuO4 Cu2+ x2-y2 x2-y2 (3d9) Cu2+x 3z2-r2 3z2-r2 xy xy yz yz zx zx Cu O Cu Cu O O t Sr J∝t2/U U t J∝t2/U Antiferromagnetism(AFM) ｔ≪Ｕ　⇒　Mott insulator Superconductivity(SC)

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

  7. motivation • t-J model AF+SC similar crystal structuresof multilayered cuprates t-J model Sample Ba2Ca3Cu4O8(FyO1−y)2

  8. motivation • t-J model T=0K ground state only single-layer Include interlayer coupling in t-J model. J=0.3t Variational Monte Carlo on t-J model SC gap Magnetic moment AF+SC MAFM ΔSC similar t-J model Sample Ba2Ca3Cu4O8(FyO1−y)2 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).

  9. t-J model for a single-layer Cu O Charge Reservoir PG = 1 0 t’ t: hopping integral J: super exchange coupling Charge Reservoir t J PG : Gutzwiller projection operator c : an annihilation operator

  10. t-J model for more than two layers Cu O Charge Reservoir t’ t⊥ J⊥ Charge Reservoir t J

  11. Electrostatic energy in the unit cell E S Charge Reservoir ρ=ex/a2 + + + + + + + + + + + + + + Gauss' law d + + + E×2S=ρS/εrε0 + + + E : electric field a : lattice constant εr : relative dielectric constant CV2/2 - - - - - - - - - - - - - - - - - - - - xi : hole concentration of IP xo : hole concentration of OP x: average hole concentration x=(xi+xo)/2 Ees : electrostatic energy d : distance between two adjacent CuO2 layers Charge Reservoir

  12. result Calculation of Δ and m SC gap Magnetic moment SC gap SC gap SC gap is decided bysingle-layer property. εr=200 εr=50 single-layer results(dashed line) εr=200 εr=50 Magnetic moment Magnetic moment IP IP Magnetic moment is also decided by single-layer property. OP OP IP IP OP Experiments on multilayer can capture the essential physics of single-layer t-J model. OP Total Hamiltonian single-layer results (dashed line)

  13. result Calculation of Δ and m Charge Reservoir SC gap SC gap εr=200 εr=50 Charge Reservoir εr=200 εr=50 single-layer results(dashed line) εr=200 εr=50 Magnetic moment Magnetic moment IP IP OP OP IP IP OP OP Total Hamiltonian Independent of εr single-layer results (dashed line)

  14. Comparison between NMR Exp. and theory discussion Sample Ba2Ca3Cu4O8(FyO1−y)2 Charge Reservoir xop over dope xip xip xop under dope estimate Charge Reservoir

  15. Comparison between NMR Exp. and theory discussion Sample Ba2Ca3Cu4O8(FyO1−y)2 Charge Reservoir xop over dope xip xip xop under dope estimate Magnetic moment calculated by theory Charge Reservoir

  16. Comparison between NMR Exp. and theory discussion Sample Ba2Ca3Cu4O8(FyO1−y)2 over dope under dope Magnetic moment Large!! Theory NMR

  17. Comparison between NMR Exp. and theory discussion Sample Ba2Ca3Cu4O8(FyO1−y)2 over dope under dope xc (NMR) =0.16 εr=50 εr=200 0.8 time IP IP xc (Theory) =0.2 OP OP HidekazuMukudaet al., J. Phys. Soc. Jpn. 81 (2012) 011008

  18. Comparison between NMR Exp. and theory discussion Sample Ba2Ca3Cu4O8(FyO1−y)2 over dope under dope Magnetic moment Theory better agreement with experiment NMR

  19. Summary Theory NMR • 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.

  20. Thank you for your attention.

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