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A. Fujimori (U. of Tokyo) M. Ikeda, T. Yoshida, K. Tanaka (U. of Tokyo)

Workshop on Electronic Structure of Emerging Materials: Theory & Experiment Velvet Country Resort, Lonavala - Khandala, February 7-10, 2007. Chemical pressure effects on the Fermi surface and band structure of electron-doped cuprate superconductors. A. Fujimori (U. of Tokyo)

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A. Fujimori (U. of Tokyo) M. Ikeda, T. Yoshida, K. Tanaka (U. of Tokyo)

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  1. Workshop on Electronic Structure of Emerging Materials: Theory & Experiment Velvet Country Resort, Lonavala - Khandala, February 7-10, 2007 Chemical pressure effects on the Fermi surface and band structure of electron-doped cuprate superconductors • A. Fujimori(U. of Tokyo) • M. Ikeda, T. Yoshida, K. Tanaka(U. of Tokyo) • T. Sasagawa, H. Takagi, K. Unozawa (U. of Tokyo) • M. Kubota, K. Ono (KEK-PF) • S. Uchida, T. Kakeshita (U. of Tokyo), H. Eisaki (AIST) • I. Terasaki, T. Sugaya,T. Mizuno (Waseda U.) • Z.-X. Shen, X.-J. Zhou, D. Lu (Stanford U.) • Z. Hussain (Advanced Light Source)

  2. Outline • Background • Tight-binding parameters: t, t’, . . . • Empirical relationship between Tc,max vs t’/t • Manifestation of t’ and its material dependence • Fermi surface • “Flat band” position. . . . . • Influence of apical oxygen on t’ • Doping dependence in LSCO • Strained film • Chemical pressure effects in electron-doped cuprates • Summary • What determines Tc,max ?

  3. t t’ t’’ Hopping parameters t, t’, t’’ in the single-band model of CuO2 plane Cu oxygen E(k)= -2t(cos kxa+cos kya) - 4t’cos kxa cos kya - 2t”(cos2kxa+cos2kya) t: nearest-neighbor t’: next nearest-neighbor t”: 2nd next nearest-neighbor t > 0, t’ < 0, t” > 0

  4. t t’ t’’ Empirical correlation between Tc ,max and next-nearest-neighbor hopping t’ Tc,max vs|t’/t| bilayer cuprates AB BB |t’/t| BB AB E. Pavarini et al., PRL ’01 D. Feng et al., PRL ‘01

  5. Outline • Background • Tight-binding parameters: t, t’, . . . • Empirical relationship between Tc,max vs t’/t • Manifestation of t’ and its material dependence • Fermi surface • “Flat band” position. . . . . • Influence of apical oxygen • Doping dependence of t’ in LSCO • Strained film • Chemical pressure effects in electron-doped cuprates • Summary • What determines Tc,max ?

  6. Fermi surface Band dispersion at half-filling (0,p) + + - t > 0 (p,0) E(k)= -2t(cos kxa+cos kya) - 4t’cos kxa cos kya - 2t”(cos2kxa+cos2kya) + + - + + - - t’ < 0 + - + + t” > 0 + + + + - - + + + + T.Tohyama and S. Maekawa, Supercond. Sci. Technol. ‘00

  7. Fermi surface LSCO YBCO BSCCO x=0.05 T. Yoshida et al., PRB ‘01. D. Feng et al., PRL ‘01, D. Lu, PRL ‘01 + + + + - - + + + + T.Tohyama and S. Maekawa, Supercond. Sci. Technol. ‘00

  8. “Flat band” at k~(p,0) Band dispersion at half-filling (0,p) + + - t > 0 (p,0) E(k)= -2t(cos kxa+cos kya) - 4t’cos kxa cos kya - 2t”(cos2kxa+cos2kya) + + - + + - - t’ < 0 E(p,0) = 4t’ - 4t” + - + + t” > 0 + + + + - - + + + + T.Tohyama and S. Maekawa, Supercond. Sci. Technol. ‘00

  9. (b) (a) La Sr CuO Bi Sr Ca R Cu O 2-x x 4 2 2 1-x x 2 8 n h = 55.5 eV T = 20 K n h = 21.2 eV T = 7 K d = x = 0.17 0.22 Intensity (arb. units) Intensity (arb. units) 0.135 0.15 0.135 0.12 BB 0.1 0.10 AB 0.05 0.07 0.025 0.03 -0.4 -0.2 0.0 -0.4 -0.2 0.0 Energy relative to E (eV) Energy relative to E (eV) F F “Flat band” at k~(p,0) BB AB average D. Feng et al., PRL ‘01 AIPES ARPES E(p,0) = 4t’ - 4t” K. Tanaka et al., PRB ‘04

  10. Flat band position E(p,0) Bi2212 LSCO Larger t’  Higher Tc,max BB average AB |E(p,0)| = |4t’ - 4t”| K. Tanaka et al., PRB ‘04

  11. Dispersion along underlying “Fermi surface” in parent insulator E(p,0) - E(p/2,p/2)  t’ + ... CCOC: CaCuCl2O2 F. Ronning et al. Science ‘98

  12. Chemical potential shift Experiment of core-level shifts Theory A. Ino et al., PRL ‘97 N. Harima et al. PRB ‘02 T. Tohyama, S. Maekawa, PRB’02

  13. Summary of material-dependent electronic structure LSCO <----------------> Bi2212, YBCO, … Fermi surface shape <-----> Flat-band position at ~(p,0) shallow <-----------> deep Band dispersion in parent insulators weak <----------------> strong Chemical potential shift pinned/slow <-------> fast small <--- |t’| ---> large

  14. t t’ t’’ Material dependence of other parameters • Hubbard (U-t, U-t-t’,U-t-t’-t”,...) model, • t-J (t-t’-J, t-t’-t”-J,…) model, • … • t’ , t’’, .. are different. • U ~ 4 eV: common • J ~ 0.1 eV: common (neutron, Raman) • t ~ 0.3 eV: common (LDA, ~ (1/2)(J/U)1/2)

  15. Outline • Background • Tight-binding parameters: t, t’, . . . • Empirical relationship between Tc,max vs t’/t • Manifestation of t’ and its material dependence • Fermi surface • “Flat band” position. . . . . • Influence of apical oxygen on t’ • Doping dependence in LSCO • Strained film • Chemical pressure effects in electron-doped cuprates • Summary • What determines Tc,max ?

  16. t t’ t’’ Effects of apical oxygen on next-nearest-neighbor hopping t’ t’ from LDA calculation E. Pavarini et al., PRL ’01

  17. c Effects of apical oxygen on next-nearest-neighbor hopping t’ “Cu 3d” Wannier orbital Cu-apical O distance influence of Cu 4s, O 2pz |t’| E. Pavarini et al., PRL ’01

  18. t t’ t’’ Effects of apical oxygen on next-nearest-neighbor hopping t’ Doping dependence of Cu-apical oxygen distance in La2-xSrxCuO4 t’ from LDA calculation x=0.3 x=0.03 E. Pavarini et al., PRL ’01

  19. Doping dependence of band structure and Fermi surface in La2-xSrxCuO4 E(k)= -2t(cos kxa+cos kya) - 4t’cos kxa cos kya - 2t”(cos2kxa+cos2kya) x T. Yoshida et al., PRB ‘06

  20. Doping dependence of Fermi surface in La2-xSrxCuO4 Experimental Fermi surface Rigid-band Fermi surface TB fit x with t’, t’’ fixed E(k)= -2t(cos kxa+cos kya) - 4t’cos kxa cos kya - 2t”(cos2kxa+cos2kya) T. Yoshida et al., JPCM, in press; cond-mat/06

  21. x=0.3 x=0.03 t t’ 2.3 t’’ Effects of apical oxygen on next-nearest-neighbor hopping t’ Doping dependence of Cu-apical oxygen distance in La2-xSrxCuO4 t’ from LDA calculation E. Pavarini et al., PRL ’01 T. Yoshida et al., JPCM, in press; cond-mat/06

  22. x=0.3 x=0.03 2.3 Effects of apical oxygen on next-nearest-neighbor hopping t’ Effects of electron correlation on observed t’ Cluster DMFT calc of effective t’/t t’ from LDA calculation extra slope E. Pavarini et al., PRL ’01 T. Yoshida et al., JPCM, in press; cond-mat/06 M. Civelli et al., PRL ‘05

  23. Outline • Background • Tight-binding parameters: t, t’, . . . • Empirical relationship between Tc,max vs t’/t • Manifestation of t’ and its material dependence • Fermi surface • “Flat band” position. . . . . • Influence of apical oxygen on t’ • Doping dependence in LSCO • Strained film • Chemical pressure effects in electron-doped cuprates • DSummary • What determines Tc,max ?

  24. Band structure and Fermi surface of strained La2-xSrxCuO4 film grown on LaSrAlO4 x = 0.15 smaller |t’/t| Da = - 0.02 A Dc = + 0.06 A TC = 44 K TC = 37 K M. Abrecht et al., PRL ‘03

  25. t t’ t’’ Material dependence of parameters • Hubbard (U-t, U-t-t’,U-t-t’-t”,...) model, • t-J (t-t’-J, t-t’-t”-J,…) model, • … • t’ , t’’, .. are different. • U ~ 4 eV: common • J ~ 0.1 eV: common (neutron, Raman) • t ~ 0.3 eV: common (LDA, ~ (1/2)(J/U)1/2)

  26. t t’ J ~ (pds)4 ~ 1/a14 t’’ t ~ (pds)2 ~ 1/a7 Variation of parameters under strain • Hubbard (U-t, U-t-t’,U-t-t’-t”,...) model, • t-J (t-t’-J, t-t’-t”-J,…) model, • … • t’ , t’’, .. are different. t’ ~ (pps) ~ 1/a2 • U ~ 4 eV: common • J ~ 0.1 eV: common (neutron, Raman) • t ~ 0.3 eV: common (LDA, ~ (1/2)(J/U)1/2)

  27.  J ~ 1/a14 |t’| > |t’| J, t > > J, t ~ (pps) ~ 1/a2 Tight-binding parameters in strained La2-xSrxCuO4 film x = 0.15 smaller |t’/t| Da = - 0.02 A Dc = + 0.06 A TC = 44 K TC = 37 K M. Abrecht et al., PRL ‘03 |t’/t| < |t’/t|

  28. Outline • Background • Tight-binding parameters: t, t’, . . . • Empirical relationship between Tc,max vs t’/t • Manifestation of t’ and its material dependence • Fermi surface • “Flat band” position. . . . . • Influence of apical oxygen on t’ • Doping dependence in LSCO • Strained film • Chemical pressure effects in electron-doped cuprates • Summary • What determines Tc,max ?

  29. Ln, Ce Cu O Chemical pressure effects in electron-doped Ln2-xCexCuO4 (Ln = La, Pr, Nd, Sm, Eu) T’-type structure without apical oxygen Lattice constants Da = - 0.05 A Dc = - 0.3 A Ln = Nd Sm Eu Chemical pressure J.T. Markert et al., PRL ‘90

  30. Chemical pressure effects in electron-doped Ln2-xCexCuO4 (Ln = La, Pr, Nd, Sm, Eu) Phase diagram Tc of Ln2-xCexCuO4 (Ln = La, Pr, Nd, Sm, Eu) Chemical pressure La Pr Nd Sm Eu AF SC Chemical pressure M. Naito et al., JJAP ‘00 J.T. Markert et al., PRL ‘90 T. Sasagawa et al., KEK MSL Report2005

  31. Fermi surfaces of electron-doped Ln2-xCexCuO4 (Ln = Nd, Sm, Eu; x = 0.15) NdCeCuO SmCeCuO EuCeCuO 1.0 1.0 AFM Brillouin Zone 1.0 MDC peak Fitted PM band Fitted AFM band ky (p/a) 0 kx (p/a) 1.0 0 1.0 0 kx (p/a) kx (p/a) 1.0 LSCO film Chemical pressure Antiferromagn. splitting: DE = 0 eV -t’/t = 0.40 DE = 0.09 eV -t’/t = 0.23 DE = 0.13 eV -t’/t = 0.21 M. Ikeda et al.

  32. Band dispersion in electron-doped Ln2-xCexCuO4 (Ln = Nd, Eu; x = 0.15) NdCeCuO SmCeCuO EDC peak MDC peak Fitted PM band Shadow band Momentum (p/a) Momentum (p/a) Chemical pressure t = 0.25 eV t = 0.36 eV or J < J M. Ikeda et al.

  33. Tight-binding parameters in Ln2-xCexCuO4 (Ln = Nd, Sm, Eu) J versus bond length t (eV) -t’/t DE (eV) NdCeCuO SmCeCuO EuCeCuO Chemical pressure Chemical pressure Y. Ohta et al., PRL ‘90 M. Ikeda et al.

  34. t t’ t’’ Empirical correlation between Tc ,max and next-nearest-neighbor hopping t’ |t’/t| vs Tc,max AB BB |t’/t| BB Nd Sm AB Eu E. Pavarini et al., PRL ’01 D. Feng et al., PRL ‘01

  35. Fermi surfaces of electron-doped Ln2-xCexCuO4 (Ln = Nd, Sm, Eu; x = 0.15) NdCeCuO SmCeCuO EuCeCuO 1.0 1.0 AFM Brillouin Zone 1.0 MDC peak Fitted PM band Fitted AFM band ky (p/a) 0 kx (p/a) 1.0 0 1.0 0 kx (p/a) kx (p/a) 1.0 LSCO film Chemical pressure Antiferromagn. splitting: DE = 0 eV -t’/t = 0.40 DE = 0.09 eV -t’/t = 0.23 DE = 0.13 eV -t’/t = 0.21 M. Ikeda et al.

  36. Outline • Background • Tight-binding parameters: t, t’, . . . • Empirical relationship between Tc,max vs t’/t • Manifestation of t’ and its material dependence • Fermi surface • “Flat band” position. . . . . • Influence of apical oxygen on t’ • Doping dependence in LSCO • Strained film • Chemical pressure effects in electron-doped cuprates • Summary • What determines Tc,max ?

  37. Which parameters govern Tc,max ? *Also under high-pressure (M. Nohara et al., PRB ’95).

  38. Summary • Electronic structure of high-Tc cuprates under different structural environment (different materials, under physical/chemical pressure, etc) can be understood by the structural dependence of the parameters t, t’, and J. • Empirical relationship between Tc,max vs vs t’/t holds for electron-doped cuprates, too. • However, in electron-doped cuprates , competition between SC and AF become serious (particularly near d-wave node). • Tc,max seems to be commonly enhanced with increasing c-axis lattice parameter.

  39. Empirical correlation between TC and Madelung potential DVA vs Tc,max DVA : Madelung potential difference between apical O and planer O short  Cu-apical O distance  long apical O  Holes goes to ….  planar O unstable  Zhang-Rice singlet  stable Y. Ohta, T. Tohyama and S. Maekawa, PRB ‘91

  40. t t’ t’’ Empirical correlation between TC and next-nearest-neighbor hopping t’ t’ from cell-perturbation calculation t’ vs Tc,max R. Raimondi et al, PRB ‘96 Tc calc. using VHS scenario: E. Dagotto et al, PRL ‘95 long  Cu-apical O distance  short weak  influence of d3z2-r2, pz strong large  -t’ small

  41. Tight-binding analysis (ECCO) A B C D E Momentum (p/a) HGFEDCBA F G H Paramagnetic band Shadow band Antiferromagnetic band t = 0.36 DE = 0.13 EDC peak MDC peak Momentum (p/a)

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