Photoemission Studies of Strongly Correlated Systems

Transcription

1 Photoemission Studies of Strongly Correlated Systems Peter D. Johnson Physics Dept., Brookhaven National Laboratory JLab March 2005

2 MgB2

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4 High T c Superconductor - Phase Diagram Fermi Liquid:-Excitations Landau-Quasiparticles [ ] 2 2 ( πk T ) Γ( ω, T ) = 2β + ω B E = η τ ω

5 dc Transport in Synthetic Metals Resistivity, [µωcm] La 1.85 Sr 0.15 CuO 4 Ioffe-Regel limit saturation Nb 3 Sn Temperature, [K] TTF-TCNQ VO 2 SrRuO Temperature, [K]

6 Drude Model of Conductivity Conductivity ne m 2 σ = * τ In a two-dimensional system σ k F l Thus the resistivity ρ is given by ρ 1 k l F = k k F or ImΣ E F

7 Spin-charge separation holon spinon e = -1, s = 0 e = 0, s = 1/2

8 R. B. Laughlin 1998 "Parallels Between Quantum Antiferromagnetism and the Strong Interactions"

9 Photoemission is an excellent probe of low energy excitations Incident Photons s p hν φ n Θ e - Photoelectrons single crystal hole sample ω = 2π η ψ f H int ψ i 2 δ ( E E hυ) f i

10 ω = 2π η ψ f H int ψ i 2 δ ( E E hυ) f i ψ ( r' ) = ψ ( r ) drg( r r ) H ( r) ( r) i ' +, ' ψ int i Spectral Response 1 A, π ( k, E) = ImG( k E) Free Electron Case:- (, E) A ( k, E) = δ ( E ) G k 1 = 0 E E k iδ 0 E k

11 We introduce the self-energy Σ to take account of interactions Green s Function G ( E) = 1 E ε E 1 ε Σ Spectral Function A 1 π ( E) = ImG( E) = 1 π Σ'' ( E ε Σ' ) 2 + ( Σ' ') 2 Photoemission peak at an energy ε - Σ Lifetime broadened to a width proportional to 2Σ =Γ

12 Photoelectron Spectrometer - + θ E K hν Resolution:- E: ~5 mev k: Å -1

13 MDCs and EDCs Science 285, 2110 (1999) Momentum Distribution Curve Energy Distribution Curve

14 MDCs and EDCs MDC width k = 2Σ'' v 0 = 1 λ Inverse Mean Free path EDC width E = ν k = η τ Inverse Lifetime = 2Σ'' Σ' 1 ω

15 Drude Model of Conductivity Conductivity ne m 2 σ = * τ In a two-dimensional system σ k F l Thus the resistivity ρ is given by ρ 1 k l F = k k F or ImΣ E F

16 Photoemission Linewidths Linewidth Γ = Γi v i 1 v i + + Γ v v f f 1 f For a 2-Dimensional initial state v i = 0 Γ = Γ i

17 a) T=70 K Intensity (arb. units) b) T (K): c) T=70 K Hydrogen exposure (L): Phys. Rev. Lett. 83, 2085 (1999) E-E F (mev)

18 Scattering Rates: ρ ρ ρ ( k, ω ) ( k + k, ω + ω ) Electron-Electron Electron-Phonon Electron-Impurity [ ] 2 2 el el ( ω, T ) = 2β ( πkbt ) + ω Γel ph( ω, T ) Γ Γel im const Γ = Γ el el + Γ el ph + Γ el im

19 Landau 1957 Fermi Liquid electron-electron scattering Scattering rate or inverse lifetime Γ = 2β[(πk B T) 2 + ω 2 ] E = η ω τ

20 A( k, ω) ImΣ( k, ω) [ ω ε ReΣ( k, ω) ] 2 + [ ImΣ( k, ω ) ] 2 k ω ω 0 α 2 F ω ω 0 ImΣ~Γ ω 0 ReΣ k A(k,ω) ω

21 Electron-Phonon Coupling Eliashberg Equation:- ( ) ( ) ( ) ( ) [ ] ' ' 2 ') ( 1 ' ' 2, 0 2 ω ω ω ω ω ω ω α π ω τ ω = f n f F d T D η η In the limit T 0 ( ) ( ) ' ' 0 2 ω ω α π ω ω d F I = Σ η

22 Temperature dependent scattering rates 1.2 Einstein mode 70 mev ImΣ Temp: Binding Energy (mev)

23 Electron-Phonon Interaction in Molybdenum 2 Im Σ (mev) E-E F (mev) κ II ( 1 ) Re Σ 2 Im Σ Re Σ (mev) E-E F (mev) Phys. Rev. Lett. 83, 2085 (1999)

24 MDCs and EDCs Science 285, 2110 (1999) Momentum Distribution Curve Energy Distribution Curve

25 Optimally Doped Bi 2 Sr 2 CaCu 2 O 8+δ Cu O EDC s Science 285, (1999) MDCs near E F

26 Abanov et al. J. Elect. Spect. 117, 129 (2001)

27 The Molybdenum Data a) T=70 K Phys. Rev. Lett. 83, 2085 (1999) Intensity (arb. units) b) T (K): c) T=70 K Hydrogen exposure (L): E-E F (mev)

28 Bi 0.5 Pb 0.5 Ba 3 Co 2 O 9+δ 60 T M 100 ρ ab (mωcm) ρ c (Ωcm) T (K) 0

29 A number of the layered strongly-correlated materials show such anisotropic transport properties: Insulating behavior T M ρ c ρ < 0 T ρ ρ c /ρ ab Metallic behavior ρ ab T ρ > 0 T

30 T=30 K -0.5 ω (ev) (a) k II (Å -1 ) Γ T=180 K detector angle (b) -0.1 Nature 417, 627 (2002) k II (Å -1 ) (c)

31 Intensity (arb. units) 30 K 95 K 180 K 230 K 30 K 230 K ω (ev) ρ ab (mωcm) T M ρ c (Ωcm) ω (ev) T (K) 0 The appearance of in-plane coherent excitations strongly correlates with the dimensional crossover observed in transport measurements 2 d k σ ω = c ( T, 0) t ( k) 2 (2π ) 2 G R ( k, ω) G A f ( ω) ( k, ω) ω Green s Function ~ Z /( ω ε iγ ) k

32 Optical Conductivity Measurements J. Tu et al.

33 The coherent excitations behave like Fermions G Γ(meV) Data: Data1_H Model: parabolic Chi^2 = y ± b ± xc 0 ±0 Γ T 2 lnt B T T(K) 0

34 Crystal structure of chain cuprates SrCuO 2 Sr 2 CuO 3

35 Intensity 4 undoped 5.5 bar 11 bar ω (ev) b) t = 0.82 J = 0.28 σ 1 (ω) [10 3 Ω -1 cm -1 ] undoped 11 bar ω [ev] ω (ev) Doping with oxygen allows the clear identification of the spinon branch

36 1D Hubbard model calculation Extended Hubbard model (half-filled, one band) ( + + cˆ ) l cˆ l+ + cˆ l+ cˆ l + U nˆ nˆ + V ( nˆ )( ) l l l 1 nˆ, σ 1, σ 1, σ, σ,, l 1 H = t + 1 l, σ l t l Dynamical density matrix renormalization group (DDMRG) Optical conductivity Neutron scatterin U V t = ev, U t = 7.8, V t = 1.3 Density-density correlation function N(q,ω)

37 Studies of 1-D Sr 2 CuO 3+δ at BN L Spinon Holon Theoretical predictions Photoemission Expt ω (ev) Spinon Holon k (π/b)

38 T. Valla T. Kidd A. Fedorov Physics Dept., BNL G.D. Gu S.L. Hulbert Q. Li Materials Science Dept., BNL A.R. Moodenbaugh N. Koshizuka ISTEC, Japan S.M. Loureiro R. Cava Princeton University

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