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High resolution ARPES studies of the strongly correlated electronic structure

High resolution ARPES studies of the strongly correlated electronic structure of high-T c superconductors. Jörg Fink Leibniz Institute for Solid State and Materials Research Dresden TU Dresden. J. F. et al. Lect. Notes Phys. 715 , 295-325 (2007), cond-mat/ 0604665. THANKS TO:.

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High resolution ARPES studies of the strongly correlated electronic structure

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  1. High resolution ARPES studies of the strongly correlated electronic structure of high-Tc superconductors Jörg Fink Leibniz Institute for Solid State and Materials Research Dresden TU Dresden J. F. et al. Lect. Notes Phys. 715, 295-325 (2007), cond-mat/ 0604665

  2. THANKS TO: Spectroscopy Group IFF, IFW Dresden Sergey Borisenko Alexander Kordyuk Andreas Koitzsch Volodymyr Zabolotnyy Dmitriy Inosov Jochen Geck Martin Knupfer Bernd Büchner Experimental collaboration and technical support Mark Golden U Amsterdam Rolf Follath BESSY G. Grazioli, S. Turchini ELETTRA Crystals and crystal characterization Helmuth Berger EPFL Lausanne Bernhard Keimer, Chengtian Lin MPI-FKF Stuttgart Konstantin Nenkov IFW-Dresden S. Ono, Yoichi Ando CRIEPI Tokyo Theory Mathias Eschrig U Karlsruhe Thomas Eckl, Werner Hanke U Würzburg Andrey Chubukov U Madison Ilia Eremin MPI PCS Dresden Thomas Dahm U Tübingen

  3. Cu O Block layer CuO2 layer Block layer T* T* TN Temperature TN Temperature TS TC AF SC Hole concentration Hole concentration UD OP OD UD OP OD Phase diagram of high-Tc superconductors MI-transition, strange normal state properties, pseudogap below T*, quantum critical point(s) ... RVB, preformed pairs, CDW, SDW, hidden order…… Dressing of the charge carriers, mass enhancement, Scattering rate, self energy S(E,k) Dressing may be connected with the glue forming the pairs

  4. t´ (p,0) (p,p) e doping t G AN N N h doping TB bandstructure of the CuO2 plane E(k) = -2t[cos(kxa)+cos(kya)]-4t´cos(kxa)cos(kya)

  5. (0,p) (p,p) B B A A G B t (0,p) (p,p) G Bilayer splitting inBi2Sr2CaCu2O8

  6. Angle-resolved photoemission (ARPES) Ekin = hn – F - EB Dressing of charge carriers

  7. Photo current, matrix element, and spectral function ReS ImS(E,k) E -W0 W0 A(E,k) ~ [E-ek-ReS(E,k)]2+[ImS(E,k)]2 |ImS| -W0 W0 E • S(E,k) self-energy • = -dReS/dE|EF • m*=(1+l)m I(E,k) ~ M(E,k) A(E,k) f(E) Engelsberg and Schrieffer, PR 131,993(1963) 1 Einstein mode, adiabatic limit (EF>> W0): EF l =1 l = 8 coherent W0 incoherent

  8. The spectral function in the superconducting state E D EF D Boson (W0) k EF l = 1 l = 8 D W0 +D EB> W0+D 1 Einstein mode: Scalapino in ‘Parks‘ (1969)

  9. Bi(Pb)2Sr2CaCu2O8+d YBa2Cu3O7-d OP OD BaO BiO CuO SrO BaO CuO2 CuO2

  10. Borisenko et al. PRL 84, 4453 (2000) Kordyuk et al. Phys. Rev. B 67, 064504 (2003) Fermi surface of Bi(Pb)2Sr2CaCu2O8+d hn= 21.2 eV (p,0)

  11. O. Andersen et al. Fermi surface of YBa2Cu3O7-d V. Zabalotnyy et al. cond-mat

  12. How to get the bare-particle bandstructure? From LDA bandstructure calculations By fitting the plasmon disperson (from EELS). Measures averaged unrenormalized Fermi velocity. Nücker et al. PRB 44, 7155 (1991); Grigorian et al. PRB 60, 1340 (1999) Assumption: S(kF,EF) small or zero. Fit of the Fermi surface by a TB bandstructure: E0(k)a,b =De -2t[cos(kxa)+cos(kya)]+4t‘cos(kxa)cos(kya)- 2t‘‘[cos(2kxa)+cos(2kya)]± t[cos(kxa)-cos(kya)]2/4  t‘/t t‘‘/t t/t • t fromImSalongthe nodal direction • KKA  ReS  E(k)-ReS= E0(k)

  13. BSCO T = 30 K (0.p) (p,p) N G Energy (eV) S´´(w) Momentum (a. u.) Dressing of the charge carriers at nodal point • Kink: • phonon • magnetic resonance mode • marginal FL, ElogE • continuum of spin fl. 3wsf • gapped cont. 2D • charge fluctuation mode • stripes Kordyuk et al. PRB 71, 214513 (2005)

  14. UD c´´ T>Tc OP -ImS OD W c´´ T<Tc (p,0) (p,p) ReS G W 2D wr DReS AN N N DImS S ~ (c*G0)E,k Re and Im of S(w) at N for OP92 at 30 and 120 K • scattering channels: • coupling to a (gapped) • continuum (spin fluctuations) • width 2J ~ 300 meV • coupling to a mode which • exists below Tc. E=W0+D= • 50-70 meV, W0~40 meV Kordyuk et al. PRB 71, 214513 (2005) Kordyuk et al. PRL 97, 017002 (2006)

  15. High-energy kink in a 2D Hubbard model Macridin, Jarrell, Maier, Scalapino cond-mat/ 0701429 Dynamical cluster quantum Monte Carlo calculation Agreement with simple calculation which couples QPs to damped spin fluctuations -> High energy kink is due to scattering from damped spin fluctuations

  16. “Waterfall” at high energies Graf et al. cond-mat/0607319 Meevasana et al. cond-mat/0612541 Valla et al. cond-mat/0610249 Chang et al. cond-mat/0610880 Xie et al. cond-mat/0607450 Pan et al. cond-mat/0610442 Wang et al. cond-mat/061049 • Crossover from QP band to MH band • Spin-charge separation • Spin fluctuations M(E,k) matrix element

  17. T=130K Doping dependence of the mass enhancement (ReS)

  18. E E E Scattering rate at low energies OP T<Tc offset, S”~ E, d-wave SC T<Tc, S”~E3, coupling to a continuum of spin excitations T<Tc, S”~E OP T>Tc, OD T>Tc, S”~E2 Evtushinsky et al. PRB 74, 172509 (2006)Dahm et al. PRB 2004

  19. T-dep. of scattering rate of Bi(Pb)2Sr2CaCu2O8+d BiO(O) Ca(Y) Cu( _) Forward (~12 meV) Unitary (~2 meV), r No decrease of the scattering rate below Tc

  20. Evidence for strong interband scattering in YBCO Borisenko et al. PRL 06

  21. Interband scattering Intraband scattering A B A A > B A B B S ~ (c*G0)w,k c of the boson which mediates the scattering is ODD with respect to the layers exchange within a bilayer!

  22. (0,p) (p,p) B B B B A A G A A B B A B (0,p) (p,p) G Dressing of the charge carriers at (p,0) hn =38eV =50eV Diff. A W0=E-D= 40 meV Kim et al. PRL 91,167002(2003)

  23. (p,p) A B B T= G A (p,0) 30K (p,-p) 120K T-dependence of kink along (p,0)-(p,p), UD sample T= 120 K mode disappears or the strong coupling to the mode is reduced

  24. -ImS ReS OP sample, sc state model functions for S Einstein mode (40 meV) + d-wave sc +continuum (ImS(w)~ w2) B A Theory Exp. ln (continuum) = 1.3 ln (mode) = 2.6 J.F. et al. PRB 74,165102 (2006)

  25. UD OP OD T<Tc B A T>Tc Coupling constant l in the n and sc state Kim et al. PRL 91,167002(2003)

  26. (p, p) G No kinks for strongly overdoped YBCO OD(31%) T = 30 K

  27. (p,p) (p,p) • N G • (p,0) YBCO OP(~17%) • (p,-p) Energy (eV) Momentum (a. u.) k-dependence BSCCO OP Energy (eV) Momentum (a. u.) strong momentum dependence

  28. AB (p,p) (0,p) N G Energy (eV) -0.2 0.0 0.2 k (A-1) ReS E -W0 W0 |ImS| -W0 W0 E Ni (S=1) and Zn (S= 0) substitution of Cu(S=1/2) I Y.Sidis et al. cond-mat/2000 V. Zabolotnyy et al. PRL 96, 037003 (2006)

  29. Ni (S=1) and Zn (S= 0) substitution of Cu(S=1/2) II (p,p) (0,p) N G T=30K lpure =1.06 l3%Ni=0.88 l1%Zn=0.76 “Magnetic Isotope Effect” Terashima et al. et al. Nature Physics 2, 27 (2006)

  30. S ~ (c*G)w,k V. Hinkov et al. ARPES YBCO INS model INS ARPES Same sample !!!

  31. c0 c = 1 - JQc0 BSCCO: quantitative spectral funtion [BZ x 0.5 eV] INS BSCO ARPES c0 ~ (G*G)w,k JQ =J0(cosQx+cosQy)+-J  Inosov et al. cond-mat/0612040

  32. (p,0) (p,p) G AN N N Summary • Nodal point: coupling to a continuum • and below Tc a weak coupling to a mode • Antinodal point: huge coupling to a • mode below Tc and a coupling to a continuum. • Energy • Momentum dependence • Temperature dependence • Doping dependence • Impurities (Zn) • Parity • INS  ARPES • ARPES  INS continuum: damped AF spin fluctuations mode: S=1 magn. resonace mode

  33. (E,k)-space for the 2D systems

  34. normal state E E EF EF Boson (W0) EB> W0 k k Auger process (e,e) Lifetime of a hole in the conduction band Bosons: phonons, spin excitations, plasmons, e-h excitations

  35. (p,p) N G (p,0) (p,-p) Temperature dependence of the scattering rate in Pb-Bi2212 OP88 • Two scattering channels: • Gee = 2b[(pkBT)2 +w2] • Below ~Tc ( or T*): transitions • from the van Hove singul. at • (p,0) to N via emission of a • magnetic resonance mode OD69

  36. Coupling of a bilayer system to a resonance mode E E UD A B A B E E k k A B A A B B k k cab cba D D Wr +D Wr +D E OD k D Wr +D b a (p,p) (p,0) (0,p) From neutron scattering: the coupling via the magnetic resonance mode occurs only via the odd channel. A  B or B  A but not A  A or B  B AB and BA coupling not possible in the very OD case. Coupling starts when A moves below EF

  37. nb s nb p ZRS ARPES of Sr2CuO2Cl2: the dispersion of a hole in an antiferromagnetic undoped CuO2 plane t-J model W t-t‘-J model W not 3 eV but only 0.5 eV Dürr et al. PRB 63,14505 (2000)

  38. Symmetry of the superconduncting gap D from ARPES (p,p) N G (p,0) (p,-p) - - + + + + - - Ding et al. PRB 54,R9678(1996) Binding Energy (meV)

  39. Origin of the Pseudogap I • Phase fluctuations of the order parameter • D = D0eif • small phase stiffness yields „cheep“ vortices Eckl et al. cond-mat/0402340

  40. Origin of the Pseudogap II • Uncertainity relation between phase and paritcle number • DN DF >~ 1 • T => 0 DF => 0, DN large, paricle number completely uncertain • BCS back-turning of the band. • T higher, DF large, DN = 0, no back-turning of the bands. • New phase-disordered pseudo-gaped bandstructure.

  41. Gap of the bonding and antibonding bands

  42. BCS-like gap in the pseudogap region??? OD76K No BCS-like gap in the pseudogap region. No horizontal dispersion. Spectral weight just disappears. Consistent with tunneling spectroscopy (no coherent peak). Coherence length in ARPES experiments: 2p/Dk= 2p/0.02A-1~30 A => superconducting fluctuations < 30 A, local Cooper pairs without phase coherence.

  43. Superstructure Pb-BSCCO BSCCO

  44. Pb or not Pb... Pb-BSCCO BSCCO

  45. Doping dependence of the scattering rate at T=25 K OD samples: e-e scattering, ~ w2 , FL behavior mode excitation at ~ 70 meV which increase with decreasing dopant concentration. OD69 Im Kordyuk et al. PRL 92, 257006 (2004)

  46. spingap coupling to a continuum resonance mode T>Tc T=Tc T<Tc The feedback process in the spin excitation scenario

  47. ReS e-ph coupling in the superconductor Pb ln=lsc = -dReS/dE|EF= 1.55 Reinert et al. PRL91,186406(2003)

  48. Doping dependence of the Fermi surface in Bi(Pb)-2212 Tc T = 300 K, hn= 21.2 eV Shape and diameter of the barrels changes with x. Kordyuk et al. Phys. Rev. B 66, 014502(2002)

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