High-T c superconductors. Parent insulators Carrier doping Band structure and Fermi surface Pseudogap and superconducting gap Transport properties

Transcription

1 High-T c superconductors Parent insulators Carrier doping Band structure and Fermi surface Pseudogap and superconducting gap Transport properties

2 High-T c superconductors Parent insulators

3 Phase diagram of high-t c superconductors CuO 2 plane T [K] 100 antiferromagnetic 10 pseudo-gap superconducting spin glass? superconducting Electron doping 0 antiferromagnetic insulator Hole doping / Cu atom

4 Zaanen-Sawatzky Sawatzky-Allen diagram = W E g ~ W charge-transfer regime CuO 2 plane 3+ charge-transfer regime p-metal d-metal Mott-Hubbard regime E g ~ U - W U = W 4+ negative- regime Mott-Hubbard regime J. Zaanen, G.A. Sawatzky, J.W. Allen, PRL 85 A.E. Bocquet et al., PRB 96

5 p-d model to effective single-band model Mott-Hubbard type insulator Charge-transfer type insulator Effective one-band model Metal d band E F -5 ev -10 ev UHB LHB Oxygen p band U: d-d Coulomb energy : p-to-d charge-transfer energy UHB Oxygen p band LHB U p-d hybr. UHB: upper Hubbard band LHB: lower Hubbard band UHB Zhang-Rice singlet band = effective LHB Oxygen p band LHB Zhang-Rice singlet (ZRS) oxygen hole M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 98 Cu spin

6 Single-band model description of CuO 2 plane in high-t C cuprates p-d model t t t Single-band (Hubbard or t-j) model t t t t-j model (t-t -t -J model) t : nearest-neighbor hopping t : next-nearest-neighbor hopping t : third-nearest-neighbor hopping

7 Electronic structure of the parent insulator Sr 2 CuO 2 Cl 2, Ca 2 CuO 2 Cl 2 Photoemission spectra AF Brillouin zone k y (π /a) B.O. Wells et al., PRL 95 F. Ronning et al., Science 98 k (π/a)

8 Electronic structure of the parent insulator Sr 2 CuO 2 Cl 2, Ca 2 CuO 2 Cl 2 Band dispersion AF Brillouin zone k y (π/a) k x (π/a) t-j model (t-t -t -J model) Exp: B.O. Wells et al., PRL 95 C. Kim et al., PRL 98 Th: T. Tohyama et al., JPSJ 00 t t

9 Electron-phonon interaction effect in Ca 2 CuO 2 Cl 2 Photoemission spectra zero-phonon line multiple-phonon lines Band dispersion chemical potential µ µ polaronic shift B A polaron µ bare electron K.M. Shen et al., PRL 05

10 Electron-phonon interaction in the insulating phase of VO 2 Simulations using independent-boson model multiple-phonon lines zero-phonon line Energy /ω 0 K. Okazaki et al. PRB 04

11 Chemical potential mystery in hole-doped and electron-doped superconductors Nd 1.85 Ce 0.15 CuO 4 µ µ La 1.85 Sr 0.15 CuO 4 =µ optical gap = 1.5 ev S. Uchida et al. µ 2.0 ev J. W. Allen et al., PRL 90 H. Namatame et al., PRB 90

12 Resonant inelastic x-ray x scattering from Ca 2 CuCl 2 O 2 expt. data U-t-t -t Hubbard model Resonant inelastic x-ray scattering Z. Hassan et al. Science 00

13 Band structure of undoped CuO 2 plane Conduction-band minimum ~ (π,0) Optical gap ~ 1.5 ev µ of Nd2CuO4 µ, chem. pot. jump ~ 0.4 ev µ of La2CuO4 polaronic shift ~ 0.5 ev Valence-band maximum ~ (π/2,π/2) Tsutsui et al. PRL 99

14 High-T c superconductors Carrier doping

15 Metal-insulator transition induced by hole doping

16 Phase diagram of La 2-x Sr x CuO 4 T [K] 100 antiferromagnetic insulator pseudo-gap metal 10 normal metal (Fermi liquid) superconductor spin glass? Hole / Cu atom

17 Initial stage of hole doping into CuO 2 plane: Chemical potential shift or pinning? UHB LHB spectral weight transfer ~< 0.4 ev µ µ shift Hole doping Ca 2-x Na x CuCl 2 O 2 Bi2212 Zhang-Rice singlet ~ effective lower Hubbard band ( LHB ) oxygen hole spectral weight transfer µ ~ 0.5 ev µ pinning La 2-x Sr x CuO 4 Cu spin

18 Hole doping into CuO 2 plane: Chemical potential shift or pinning? µ pinning in La 2-x Sr x CuO 4 µ shift in Ca 2-x Na x CuCl 2 O 2 LHB LHB LHB QP QP LHB LHB QP k y (π/a) AF Brillouin zone T. Yoshida et al., PRL 03 π/2,π/2 k (π/a) K.M. Shen et al., PRL 05

19 Chemical potential shift in high-t c cuprates from core-level photoemission Ca 2-x Na x CuO 2 C 2 La 2-x Sr x CuO 4 Bi2201 YBa 2 Cu 3 O y Nd 2-x Ce x CuO 4 µ shift µ pinning Large µ shift in overdoped region normal Fermi liquid Electron doping Hole doping / Cu A. Ino et al., PRL 79, 97 N. Harima et al., PRB 01 N. Harima et al., PRB 03 H. Yagi et al.,

20 Chemical potential shift in the presence of charge stripes?

21 Spectral weight transfer induced by hole doping from O 1s x-ray x absorption spectra Doping dependence Angular dependence QP µ µ UHB QP spectral weight transfer spectral weight transfer QP UHB Consistent with Zhang-Rice singlet UHB oxygen hole d(x 2 -y 2 ) - p x, p y C.T. Chen et al., PRL 91, 92 Cu spin

22 Spectral weight transfer induced by hole doping µ shift overdoped --> Fermi liquid Hole doping µ shift/pinning spectral weight transfer LHB(ZRS) UHB H. Eskes et al., PRL 91 effective Hubbard model

23 High-T c superconductors Band structure and Fermi surface

24 Phase diagram of La 2-x Sr x CuO 4 T [K] 100 antiferromagnetic insulator pseudo-gap metal 10 normal metal (Fermi liquid) superconductor spin glass? Hole / Cu atom

25 Spectral function of correlated Fermi liquid quasi-particle (QP) peak incoherent part incoherent part k F k F Fermi surface k F is defined by * Discontinuity in n k * E F crossing of infinitely sharp QP peak A. Damascelli et al., RMP 01

26 Fermi surface and d-wave superconducting gap/pseudogap pseudogap in high-t C cuprates CuO 2 plane t t t t electron d-wave order parapeter: (k) = 0 (cosk x a -cosk y a) hole Node Anti-node t t t Band structure and Fermi surface: E(k) = -2t(cos k x a+cos k y a) - 4t cos k x a cos k y a -2t (cos2k x a+cos2k y a)

27 Angle-Resolved Photoemission Spectroscopy ARPES EF below EF Band dispersion k ky Fermi sruface kx

28 Advanced Light Source ARPES beamline SGM beamline + Scienta SES-2000 X. J. Zhou, Z.-X. Shen, Z. Hussain

29 Stanford Synchrotron Radiation Laboratory ARPES beamline 5-45 Scienta SES-2000 NIM beamline D. Liu, C. Kim, Z.-X. Shen

30 ARPES: Fermi surface and band mapping hν = 55.5 ev EF E φ EF θ E k T. Yoshida, Thesis

31 Fermi surface electron hole Tight binding fit: E(k)= -2t(cos k x a+cos k y a) -4t cos k x a cos k y a -2t (cos2k x a+cos2k y a) x Tight-binding fit Intensity peak in k-space T. Yoshida et al.

32 Band dispersion in the nodal direction: Quasi-particle Energy relative to E F (ev) x = 0.03 x=0.07 x=0.15 (π/2,π/2) (π/2,π/2) (π/2,π/2) (π/2,π/2) x=0.22 Tight-binding fit Fermi velocity of nodal QP is doping-independent! X.J. Zhou et al., Nature 03 T. Yoshida et al.

33 Pseudogap/superconducting gap in the anti-nodal nodal region Energy relative to E F (ev) pseudogap pseudogap superconducting gap Tight binding fit T. Yoshida et al.

34 Remnant Fermi-surface crossing in lightly-doped La 2-x Sr x CuO 4 pseudogap pseudogap T. Yoshida et al.

35 Luttinger sum rule is satisfied! Experimental Fermi surface Luttinger sum rule hole 1+ x FS electron 1- x FS x FS = x x x violated! La 2-x Sr x CuO 4 Ca 2-x Na x CuO 2 C 2 Tight-binding fit Intensity peak In k-space T. Yoshida et al.

36 High-T c superconductors Pseudogap and superconducting gap

37 Pseudogap and Fermi arc electron hole Tight binding fit: E(k)= -2t(cos k x a+cos k y a) -4t cos k x a cos k y a -2t (cos2k x a+cos2k y a) x Tight-binding fit Intensity peak in k-space T. Yoshida et al.

38 Pseudogap behaviors of La 2-x Sr x CuO 4 Superfluid density Carrier number Y.J. Uemura et al., PRL 89 Pauli susceptibility H. Takagi et al., PRB 89 Electronic specific heat T. Nakano et al., PRB 94 AFI AF SC metal N. Momono et al., JPSJ 03 Hole doping x

39 Density of QP s and electronic specific heats Density of QP s from ARPES Density of QP s at E F compared with specifit heat γ γ: N. Momono et al., Physica C 94

40 Density of QP s and electronic specific heats Fermi arc length Density of QP s at E F compared with specifit heat γ γ: N. Momono et al., Physica C 94

41 Superconducting gap and small pseudogap in La 2-x Sr x CuO 4 Superconducting gap /small pseudogap (Large) pseudogap k~(π,0) Superconducting gap /small pseudogap A. Ino et al., PRB 02

42 High-T c superconductors Transport properties

43 Drude fomulae of electrical conductivity Equation of motion for charge carriers m*dv/dt = -ee - m*v/τ = 0 v = eeτ/m* j = nev = σe = ne 2 Eτ/m* conductivityσ = ne 2 τ/m* = ne 2 l/hk F = ne 2 /hk F k resistivity: ρ = 1/σ m*v F = hk F, τ = l/v F l = 1/ k can be measured by ARPES

44 Fermi velocity, Fermi momentum, and mean-free path from ARPES data Fermi velocity v F k kink? T. Yoshida et al., PRL 03 k F cf) Mn oxide: Y. D. Chuang et al., Science 01 Effective mass m*= hk F /v F Scattering rate 1/τ =v F /l Mean-free path l = 1/ k ~ 30 A can be measured by ARPES σ = ne 2 /hk F k = xe 2 /hk F k ρ ~ 3.7 mωcm cf) ρ DC ~ 4.4 mωcm

45 Boltzmann transport k y E (π,π) k F θ v F τ = l l = 1/ k k x

46 Doping and momentum dependence of MDC width Mean free path l= 1/ k ~7>>1/k F Intensity (arb. units) ~ x=0.03 x=0.063 x=0.15 x=0.22 x=0.30 k Momentum (π/a) α [degree] T. Yoshida et al.,

47 Boltzmann transport on the Fermi arc Complete Fermi surface Fermi arc Ω ρ ρ Ω ρ ρ Fermi arc length T. Yoshida et al., Experimental broadening in k-space 1/τ tr < 1/τ ARPES

48 Unusual metallic transport in lightly-doped cuprates Metallic resistivity well exceeds the Ioffe-Regel limit Ioffe-Regel limit k F l ~ 1 Mean-free path l is shorter than 1/k F ~ 2 A in spite of well-defined Fermi surface? Due to pseudogap/fermi arc Y. Ando et al. PRL 01

49 Kink due to electron-phonon interaction in hole-doped cuprates ε k ε k /(1+λ) ε k ε F ω D k F Aschcroft and Mermin, Solid State Physics A. Lanzara et al. Nature 01