Understanding the Tc trends in high Tc superconductors. Kazuhiko Kuroki

Transcription

1 NQS Yukawa Inst. Understanding the Tc trends in high Tc superconductors Dept. of Physics, Osaka University Kazuhiko Kuroki Collaborators cuprates : H. Sakakibara(RIKEN), K. Suzuki(Osaka), H. Usui(Osaka), K. Kusakabe(Osaka), I. Maruyama(Fukuoka), S. Miyao (Osaka), R.Arita (RIKEN), H. Aoki (Tokyo), D.J. Scalapino (Santa Barbara) iron pnictides : K. Suzuki(Osaka), H. Usui(Osaka), H. Nakata (Osaka), H. Sakakibara(RIKEN), S.Iimura (TIT), Y.Sato(TIT), S.Matsuishi(TIT), H. Hosono(TIT)

2 Two high Tc families cuprates Iron pnictides Fe As ΔE " " dx y 2 2 " d z 2 " La O t 2 As t 1 Fe dxy

3 Approaches to unconventional superconductivity material elements, structure Wien2k VASP first principles band structure wannier90 model based on maxloc Wannier Many body analysis, superconductivity eigenvalue

4 Band calculation and maxloc Wannier VASP : G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); G. Kresse and J. Furthm uller, ibid. 54, 11169(1996); [ Wien2k : P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, Wien2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Vienna University of Technology, Wien, 2001). MaxLoc Wannier : N. Marzari and D. Vanderbilt, Phys. Rev. B 56, (1997); I. Souza, N. Marzari, andd.vanderbilt, ibid. 65, (2001); Wannnier90 : Wannier functions are generated by the code developed by A. A. Mostofi, J. R. Yates, N. Marzari, I. Souza, and D. Vanderbilt ( Wien2wannier : J. Kunes, R. Arita, P. Wissgott, A. Toschi, H. Ikeda, and K. Held, Comput. Phys. Commun. 181, 1888 (2010).

5 Maximally Localized Wannier functions Z 2 La 4f XZ Fe 3d YZ O 2p As 4p Y x 2 -y 2 XY 6 electrons/10 orbitals Uses the code developed by Mostofi et al. X As 4p are effectively included

6 Multiorbital model on-site interactions U U -J J intra orbital inter orbital Hund s coupling pair hopping U=3 ev taken for cuprates, 1.5 to 2eV taken for pnictides

7 FLEX (Fluctuation Exchange) Bickers et al, PRL 62 (1989) 961 G Dyson s eq. self-consistently self-energy. fluctuation mediated effective pairing interaction (mainly spin) linearized Eliashberg eq:

8 Eigenvalue of the Eliashberg eq. 1 λ λ Β T c A T c B case B if λ Β > λ Α then T c B > T c A λ Α case A T λ(τ)=1 at T=T c, λ at a fixed temperature(t=0.01ev here) used as a measure of T c

9 spin fluctuation based pairing, weak coupling approach; the results can intuitively understood discuss the T c trend within a family of superconductors, (not the absolute values) fix the electron-electron interactions assuming that their variance is not so large within a family, and extract the effect of the band structure variance

10 Two high Tc families cuprates Iron pnictides Fe As ΔE " " dx y 2 2 " d z 2 " La O t 2 As t 1 Fe dxy

11 Tc trend in the cuprates: a correlation with the madelung energy apical O Cu in-plane O ΔV A =madelung energy difference between apical O and in-plane O Y. Ohta, T. Tohyama, and S. Maekawa, Phys. Rev. B 43, 2968 (1991)

12 Tc trend in the cuprates: a correlation with the Fermi surface t 2 E. Pavarini et al., PRL 87, (2001) t 1 r ~ t 2 /t 1

13 Tc trend in the cuprates: a correlation with the Fermi surface small r square FS large r rounded FS E. Pavarini et al., PRL 87, (2001) r ~ t 2 /t 1

14 Related theoretical studies T. Moriya and K. Ueda, JPSJ. 63, 1871 (1994) T. Maier et al, PRL 85, 1524 (2000) C.T. Shih et al, PRL 92, (2004) M. Mori et al, PRL 101, (2008) S. Shinkai et al, JPSJ 75, (2006) C. Weber et al., PRB (2010) P.R.C. Kent et al, PRB 78, (2008) H. Sakakibara et al, PRL 105, (2010), PRB 85, (2012) L. Hozoi et al, Sci. Rep. 1, 65 (2011) S. Uebelacker and C. Honerkamp, PRB 85, (2012) C. Weber et al, EuroPhys. Lett. 100, (2012) H. Yokoyama and M. Ogata, JPSJ 82, (2013)

15 dz 2 component mixture in the cuprates usually consider only dx 2 -y 2 orbital we have explicitly considered dz 2 orbital H. Sakakibara, KK et al, PRL 105, (2010) width of Green line:strength of d z2 orbital character La214 Hg1201 Γ Γ Γ Γ

16 dz 2 component mixture in the cuprates width of green line:strength of d z2 orbital character La214 Hg1201 Γ Γ Γ Γ small r Large r

17 Two orbital model ΔE " " dx y 2 2 " " d z 2 present model Cu x d 2 y 2 Op σ Cud z 2 Op z [apical] on site Δ E = E E x y z on site measures the contribution of the d z2 orbital to the Fermi surface

18 Influence of ΔE variance=dz 2 mixture d-wave SC eigenvalue vary ΔE directly by hand in the two orbital model of La214 essentially single orbital drives d-wave SC La ΔE " " dx y 2 2 " d z 2 " Sakakibara et al, 2010 does not favor d-wave SC larger dz 2 mixture less Fermi surface roundness, smaller r lower T c because dz 2 orbital degrades d-wave SC

19 Correlation between the oxygen height and the d z 2 orbital La [apical] Hg h h O =2.42Å low h O =2.78Å O high d x2-y2 E=0.91eV small E=2.19eV large d x2-y2 d z2 d z2

20 Another structural origin for the material dependence of DE pushes up the p z level by coulomb repulsion between neighboring apical oxygen apical oxygen ΔE p ΔE Op σ Op z " " dx y 2 2 " d z 2 " [apical] Cu x d y 2 2 Cud z 2

21 H.Sakakibara, KK et al, PRB 85 (2012) evaluated via 3d 5+ 2p 3 4=17 orbital model [apical]

22 Bi-layer cuprates width of green line:strength of d z2 orbital character small ΔE large H. Sakakibara, KK et al., PRB 89, (2014)

23 Consistency with Maekawa plot d-wave eigenvalue of the two orbital model Sakakibara, KK et al. unpublished 3d p 3 6=28 orbital model ΔV A =madelung energy difference between apical O and in-plane O Y. Ohta, T. Tohyama, and S. Maekawa, Phys. Rev. B 43, 2968 (1991) [apical]

24 Understanding Pavarini plot d-wave eigenvalue of the two orbital model experimental H. Sakakibara, KK et al., PRB 89, (2014) evaluated by single orbital model r =(t 2 +t 3 )/t 1 E. Pavarini et al., PRL 87, (2001)

25 Understanding Pavarini plot single orbital model = dx 2 -y 2 only [dz 2 is implicitly considered in the dx 2 -y 2 Wannier orbital] H. Sakakibara, KK et al., PRB 89, (2014) E. Pavarini et al., PRL 87, (2001)

26 Two high Tc families cuprates Iron pnictides Fe As ΔE " " dx y 2 2 " d z 2 " La O t 2 As t 1 Fe dxy

27 Iron-based Superconductors Fermi surface nesting à spin fluctuationà s± pairing As Fe La (π,0) hole O + - hole (0,π) - electron + hole Mazin et al, 2008 KK et al 2008 five orbital model KK et al, PRL 2008 Δ(k) cos(kx)cos(ky)

28 Fourier transformation to real space: pnictides cuprates S±à 2 nd neighbor pairing cos(k x )cos(k y ) d-waveà 1st neighbor pairing cos(k x ) ー cos(k y )

29 Largely electron-doped 1111 systems LaFeAsO 1-x H x La La S.Iimura et al.,nat. Comm (2012)

30 Heavily electron-doped 1111 Iron-based SC LnFeAsO 1-x H x SmFeAs 1-y P y O 1-x H x As0.47P0.53 S.Iimura et al.,nat. Comm (2012) S. Matsuishi et al, PRB (2014) As

31 Doping dependence of the bond angle parallel shift by Ln substitution

32 Doping rate - bond angle linked model l Hypothetical La1111 l Consider linear bond angle variation with doping l Doping rate x=0.05 ~ 0.5, increment of 0.05 l Parallel shift of Δα = - 3 to +2 with respect to La, increment of 1 ; corresponds to Ln or Pn substitution La + electron doping - O As Fe corresponds to Ln or Pn substitution +

33 Doping rate - bond angle linked model l Band calculation VASP, GGA- PBEsol, cut- off 550 ev, 1000 k- points l Virtual crystal approximation, mix O : F =1- x : x, similar role of F and H Iimura et al.,nat. Comm (2012) l 5 orbital model [Wannier90] for each case (6x10=60 models) La + electron doping - O As Fe corresponds to Ln or Pn substitution +

34 Non-rigid band Δα=0 (original La1111) electron doping rate varied x=0.05à 0.50 thickness = d xy orbital component

35 Doping dependence of λ for s±wave s-wave SC eigenvalue orbital independent interaction U=1.3, U=U/6, T=0.005 [ev] Δα= K.Suzuki, KK et al, PRL 113, (2014)

36 Doping dependence of λ for s±wave s-wave SC eigenvalue orbital independent interaction U=1.3, U=U/6, T=0.005 [ev] Δα= K.Suzuki, KK et al, PRL 113, (2014)

37 Intraorbital spin susceptibility cannot be understood from the Fermi surface evolution

38 Prioritized diagonal hopping t 2 As t 1 Fe dxy t 1 rapidly decreases with doping! t 1 <t 2 for large doping : prioritized diagonal motion larger Δα requires more doping for t 1 <t 2 cf. material dependence of the reduction of t 1 studied also in T. Miyake et al., JPSJ 79, (2010), O.K. Andersen and L. Boeri, Ann. Phys. 523 (2011), Z.P. Yin et al., Nat. Mat. 10, 932 (2011)

39 Diagonal hopping : favors (π,0) spin fluctuation and s±sc t 2 s± t 1

40 Prioritized diagonal hopping opposite signs + La O electron doping - As Fe destructive quantum interference direct>0 between direct and indirect paths Fe3d Fe3d As4p +

41 Prioritized diagonal hopping opposite signs + La O electron doping - As Fe + destructive quantum interference between direct and indirect paths Fe3d indirect<0 Fe3d As4p

42 Prioritized diagonal hopping opposite signs + La O electron doping - As Fe + destructive quantum interference between direct and indirect paths Fe3d when doping increases. Fe3d As4p

43 Prioritized diagonal hopping - - destructive quantum interference between direct and indirect paths

44 Heavily electron-doped 1111 Iron-based SC eigenvalue of the Eliashberg eq. s± pairing

45 calculation for actual materials nesting prioritized diagonal motion

46 Prioritized diagonal motion in other materials alkali metal/ ammonia intercalated FeSe T c ~44K electron doping rate P. Hirschfeld, R. Valenti et al, arxiv

47 Cuprates & Fe-based : commonalities and differences xz/yz/xy orbital nesting and xy t 2 >t 1 cooperating cuprates x 2 -y 2 xz/yz/(xy) xy x 2 -y 2 / z 2 x 2 -y 2 and z 2 orbitals competing Iron-based SC

48 t 1 <t 2 pnictides cuprates t 1 >t 2 S±à 2nd neighbor pairing cos(k x )cos(k y ) d-waveà 1st neighbor pairing cos(k x ) ー cos(k y )

49 Conclusions aim to extract important microscopic parameters that governs the Tc trend cuprates ΔE : dz 2 orbital mixture reduces the FS warping and Tc simultaneously; origin of both Maekawa and Pavarini plots iron-based SC t 1 -t 2 : non-rigid band feature, prioritized diagonal motion upon electron doping multiorbitals cooperate in Fe-based, compete in cuprates, consistency between real space and momentum space in the pairing state