High-T c superconductors

Transcription

1 High-T c superconductors Parent insulators Carrier doping Band structure and Fermi surface Pseudogap, superconducting gap, superfluid Nodal states Bilayer, trilayer Stripes

2 High-T c superconductors Parent insulators

3 p-d model to effective single-band model Zhang-Rice singlet oxygen hole Cu spin

4 Electronic structure of the parent insulator Sr 2 CuO 2 Cl 2 B.O. Wells et al., PRL 95

5 Electronic structure of the parent insulator Ca 2 CuO 2 Cl 2 F. Ronning et al., Science 98

6 La 2-x Sr Valence-band shift between hole-doped Sr x CuO 4 and electron-doped Nd 2-x Ce x CuO 4 Nd1.85Ce0.15CuO4 EF EF optical gap = La1.85Sr0.15CuO4 Allen et al., PRL 90 Namatame et al., PRB 90

7 Core-level shift between Sr x CuO 4 and Nd 2-x Ce x CuO 4 La 2-x Sr 400 mev 140 mev µ (ev) µ Harima et al., PRB 01

8 Chemical potential shift in La 2-x Sr x CuO 4 and Nd 2-x Ce x CuO K.Yamada et.al, unpublished K.Yamada et.al, PRB 57,6165(1998) 0.20 Incommensurability ε Nd 2-x Ce x CuO 4 La 2-x Sr x CuO Chemiclal Potential Shift µ ( ev ) electron hole Doping Level Ino et al., PRL 97 Harima et al., PRB 01

9 Resonant inelastic x-ray scattering from Ca2CuCl CuCl2O2 expt. data U-t-t -t Hubbard model Resonant inelastic x-ray scattering Z. Hassan et al. Science 00

10 Band structure of undoped CuO 2 plane Optical gap ~ 1.5 ev µ of Nd2CuO4 µ, Transport gap ~ 0.5 ev µ of La2CuO4 Tsutsui et al. PRL 99

11 High-T c superconductors Carrier doping

12 Metal-insulator transition induced by hole doping

13 Crystal structures

14 Phase diagram of La 2-x Sr x CuO % spin glass

15 Phase diagram of Bi 2 Sr 2-x R x CaCu 2 O 8+ (R = Er,, Pr) 8+δ Ca -> Er, Pr from thermopower, Hall coeff Takemura, Kitajima, Sugaya, Terasaki, J. Phys. Cond. Mat. 00

16 Evolution of DOS with hole doping

17 Evolution of DOS with hole doping: O 1s X-ray absorption spectra of La 2-x Sr x CuO 4 Doping dependence Angular dependence Consistent with Zhang-Rice singlet d(x 2 -y 2 ) - p x, p y oxygen hole C.T. Chen et al., PRL 91, 92 Cu spin

18 Photoemission from La 2-x Sr x CuO 4 : (Large) pseudogap in underdoped region Density of states at E F Angle-integrated photoemission spectra ρ(µ) PG magnitude of pseudogap γ, χ cs : T. Nakano et al., PRB 94 T H : Y. Hwang et al., PRL 94 PES: A. Ino et al., PRL 98

19 Chemical potential shift in La 2-x Sr x CuO 4 and Nd 2-x Ce x CuO K.Yamada et.al, unpublished K.Yamada et.al, PRB 57,6165(1998) 0.20 Incommensurability ε Nd 2-x Ce x CuO 4 La 2-x Sr x CuO Chemiclal Potential Shift µ ( ev ) electron hole Doping Level Ino et al., PRL 97 Harima et al., PRB 01

20 Chemical potential shift: Fermi-liquid vs pseudogap behaviors

21 QP-QP repulsion F s o and mass enhancement m*/m b

22 Chemical potential shift in the presence of charge stripes

23 Microscopic phase separation as the origin of chemical potential pinning and pseudogap

24 High-T c superconductors Band structure and Fermi surface

25 Angle-resolved photoemission spectroscopy (ARPES) EDC k MDC

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

27 Stanford Synchrotron Radiation Laboratory ARPES beamline 5-4 Scienta SES-2000 NIM beamline D. Liu, C. Kim, Z.-X. Shen

28 Correlated Fermi liquid 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

29 Band structure and Fermi surface in La 2-x Sr x CuO 4 EDC MDC tight-binding fit d x2-y2 symmetry pseudogap T. Yoshida et al. PRB 2001

30 (Small) pseudogap on Fermi surface in normal state k F k F Minimum gap locus in underdoped Bi 2 Sr 2 CaCu 2 O 8 H. Ding et al., PRL 97

31 High-T c superconductors Pseudogap, superconducting gap, superfluid

32 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

33 Peak at k ~ (π,(, 0) and superfluid density in Bi 2 Sr 2 CaCu 2 O 8+δ supercond. peak ratio superfluid density DOS at E F condensation energy D. L. Feng et al., Science 00

34 High-T c superconductors Nodal states

35 Quasi-particles along the node direction Bi 2 Sr 2 CaCu 2 O 8 T. Valla et al., Science 99

36 Metallic nodal quasi-particles in La 1.97 Sr 0.03 CuO 4 Lower Hubbard band

37 Metallic transport in spin-glass and antiferromagnetic phases of La 2-x Sr x CuO 4 Electrical resistivity Hall mobility Metallic, but k F l << 1. x dependence is largely due to n Y. Ando et al. PRL. 01

38 Nodal quasi-particle forming a Fermi arc in La 1.97 Sr 0.03 CuO 4 La 1.97 Sr 0.03 T. Yoshida et al., cond-mat/02

39 Fermi surface to Fermi arc in La 2-x Sr x CuO 4 as x 0 (π,π) Γ Γ T. Yoshida et al.

40 Fermi arc is a half hole pocket? Underdoped Bi2212 SU(2) theory D.S. Marshall et al, PRL 96 X.G. Wen and P.A. Lee, PRL 96

41 Fermi arc at T C < T < T* T < Tc Tc < T < T* T* < T M.R. Norman et al., Nature 98 Origin of the Fermi arc Staggered flux phase? X.-G. Wen and P.A. Lee, PRL 96 d-density wave? S. Chakravarty et al., PRB 2001 Circulating current phase? C. M. Varma

42 n ~ x behaviors in high-t c cuprates Hall effect: n =1/eR H x Superfluid density n s x n s Drude weight in optical conductivity x? S. Uchida, Y. Tokura, H. Takagi, Y.J. Uemura et al., PRL 89

43 Spectral weight of nodal quasi-particle Carrier number? La 2-x Sr x CuO 4 spectral weight of nodal QP carrier number n Hall = 1/eR H T. Yoshida et al., cond-mat/02

44 Normal-state transport by nodal quasi particles La 2-x Sr x CuO 4 ρ = m*/ ne 2 τ k = 0.033(Å -1 ) λ = 1/ k ~ 30Å m*~ 3m e τ = λ /v F ~15 fs if we assume n =n PES or Z NQP ρ ~ 3.7 mωcm agrees with transport data: ρ ~ 4.4 mωcm

45 Doping dependence of normal-state transport La 2-x Sr x CuO 4 n = x n = z NQP ~ n PES (~ n Hall ) n = 1-x transport data T. Yoshida et al., cond-mat

46 Spectral weight transfer between coherent and incoherent parts CuO 2 plane Zhang-Rice singlet (LHB) UHB LHB D Hubbard U UHB coherent incoherent tight-binding fit T. Yoshida et al., cond-mat µ coherent incoherent

47 No band narrowing (m*~ const!) as x 0 La 2-x Sr x CuO 4 e.g., variational Monte-Carlo for RVB state by A. Paramekanti et al., PRL 2001 X.J. Zhou et al.

48 No band narrowing (m*~ const!) as x 0 Z 0 ==> strong ω-dependence of Σ(k,ω) m* = m k /Z ~ const ==> m k 0 ==> strong k-dependence of Σ(k,ω) pseudogap: N(µ)=(m k /m 0 ) N band (µ) 0 ==> m k 0 ==> strong k-dependence of Σ(k,ω) Strongly k-dependent electronic structure (unlike 3D)

49 Strong electron-phonon interaction in all 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

50 Kink due to electron-phonon interaction Surface state on Be metal A. Lanzara et al., Nature 01 M. Hengsberger et al., PRL 99

51 High-T c superconductors Bilayer, triplayer

52 Bilayer splitting CuO2 bilayer - Bilayer splitting is reruced in underdoped samples - No doping dependence in bilayer splitting (Y.-D. Chuang et al., cond-mat/01 ) bilayer splitting D.L. Feng et al. PRL 01 P.V. Bogdanov et al, PRB 01 Theory: S.E. Barnes and S. Maekawa, cond-mat/01

53 Gap and coherence peak in trilayer Bi2223 Smaller bilayer splitting - Both pairing strength and phase coherence is important for high Tc - Interlayer tunneling is irrelevant to high Tc D.L. Feng et al., cond-mat/01

54 High-T c superconductors Stripes

55 Phase diagram of high-t c cuprates diagonal stripes = spin glass 4a A B dynamical vertical stripes C Fermi surface Fermi Surface D k y % k x k x SG 2 6 X. J. Zhou et al., Science 99

56 Observation of incommensurate neutron peaks - vertical and diagonal stripes in LSCO diagonal stripes static K. Yamada et al., PRB 97 S. Wakimoto et al., PRB 99, 00 M. Matsuda et al., PRB 00 vertical stripes dynamical Nd subst. static

57 1D D Fermi surface segments and 2D Fermi surface with nodal quasi-particles 1.0 a Nd-LSCO(Sr0.10) b Nd-LSCO(Sr0.15) k y (π) c d D Fermi surface segment X.J. Zhou et al., PRL LSCO(Sr0.15) k x (π) 2D Fermi surface Energy window at E F ~ 30 mev