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Physics of correlated electron materials: Experiments with photoelectron spectroscopy

h. e -. Summer School on Ab-initio Many-Body Theory , San Sebastian, 25-07-2007. Physics of correlated electron materials: Experiments with photoelectron spectroscopy. Ralph Claessen U Würzburg, Germany. h. e -. Outline : Photoemission of interacting electron systems

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Physics of correlated electron materials: Experiments with photoelectron spectroscopy

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  1. h e- Summer School on Ab-initio Many-Body Theory, San Sebastian, 25-07-2007 Physics of correlated electron materials:Experiments with photoelectron spectroscopy Ralph Claessen U Würzburg, Germany

  2. h e- • Outline: • Photoemission of interacting electron systems • Mott-Hubbard physics in transition metal oxides • Correlation effects in 1D • TiOCl: Challenges for ab initio many-body theory

  3. interacting electrons non-interacting electrons ARPES  spectral function ARPES  band structureE(k) Angle-resolved photoelectron spectroscopy

  4. Photoemission: many-body effects electron-electron interaction Ekin h photoelectron: "loss" of kinetic energy due to excitation energy stored in the remaining interacting system !

  5. Many-body theory of photoemission Fermi´s Golden Rule for N-particle states: with N-electron ground state of energy EN, 0 N-electron excited state of energy EN, s, consisting of N-1 electrons in the solid and one free photoelectron of momentum and energy  in second quantization one-particle matrix element

  6. Many-body theory of photoemission Fermi´s Golden Rule for N-particle states: SUDDEN APPROXIMATION: Factorization ! sth eigenstate of remaining N-1 electron system photoelectron Physical meaning:photoelectron decouples from remaining system immediately after photoexcitation, before relaxation sets in

  7. Many-body theory of photoemission Fermi´s Golden Rule for N-particle states: SUDDEN APPROXIMATION: Factorization ! sth eigenstate of remaining N-1 electron system photoelectron Physical meaning:photoelectron decouples from remaining system immediately after photoexcitation, before relaxation sets in

  8. The ARPES signal is directly proportional to the single-particle spectral function otherelectrons single-particle Green´s function phonons ? spin excitations Many-body theory of photoemission If additionally Mif~ const in energy and k-range of interest:

  9. Ekin E u* g H2 L. Åsbrink, Chem. Phys. Lett. 7, 549 (1970) Many-body effects in photoemission Example: Photoemission from the H2 molecule

  10. Ekin E u* g H2 L. Åsbrink, Chem. Phys. Lett. 7, 549 (1970) Many-body effects in photoemission Example: Photoemission from the H2 molecule electrons couple to proton dynamics ! photoemission intensity: electronic-vibrational eigenstates of H2+:

  11. Ekin E u* g H2 L. Åsbrink, Chem. Phys. Lett. 7, 549 (1970) Many-body effects in photoemission Example: Photoemission from the H2 molecule Franck-Condon principle ħ0 v = 2 v = 1 v = 0 eneregy v' = 0 proton distance

  12. assuming Lorentzian lineshapes the total width is given by tot ~ eV ~ meV Caveat: Effect of photoelectron lifetime ARPES intensity actually convolution of photoholeand photoelectron spectral function e energy h spectrum dominated by photo-electron linewidth unless h slope  low-dim systems ! k

  13. h e- • Outline: • Photoemission of interacting electron systems • Mott-Hubbard physics in transition metal oxides • Correlation effects in 1D • TiOCl: Challenges for ab initio many-body theory

  14. cubic perovskites perovskite-like anatas rutile spinel Transition metal oxides oxides of the 3d transition metals: M = Ti, V, … ,Ni, Cubasic building blocks: MO6 octahedraelectronic configuration: O 2s2p6 = [Ne] M 3dn O2- quasi-atomic,strongly localized

  15. U t Hubbard model kinetic energy,itinerancy local Coulomb energy,localization

  16. A()   atomic limit: Mott insulator U  Hubbard model with half-filled band (n=1) d1 configuration (Ti3+, V4+) k-integrated spectral function for limiting cases (non-interacting bandwidth W  t ): U/W << 1 U/W >> 1 one-electron conduction band: metal W 

  17. U   Photoemission of a Mott insulator TiOCl Ti 3d1 O 2p / Cl 3p d1  d0LHB d1  d2UHB

  18. evolution of quasiparticle peak for local self-energy () Bandwidth-controlled Mott transition dynamical mean-field theory dynamical mean-field theory of the Hubbard model band metal correlated metal insulator

  19. QP LHB Photoemission of a correlated d1 metal A. Fujimori et al., PRL 1992 O 2p V 3d1 LHB QP incoherentweight coherentexcitations

  20. Spectral evolution through the Mott transition photoemission DMFT LHB QP UHB LHB QP A. Fujimori et al., PRL 1992

  21. photoelectron mean free path l(Ekin) Ekin~ h h surface (Ekin) 900 eV 275 eV 40 eV bulk Surface effects in photoemission A. Sekiyama et al., PRL 2004 CaVO3 QP LHB

  22. Surface effects in photoemission A. Sekiyama et al., PRL 2004 CaVO3 QP LHB • at surface reduced atomic coordination • effective bandwidth smaller:Wsurf < Wbulk • surface stronger correlated:U/ Wsurf >U / Wbulk

  23. soft x-ray PES (h ~ several 100 eV) S.K. Mo et al., PRL 90, 186403 (2003) surface (40 eV) ~ 5 Å (800 eV) ~ 15 Å unit celld ~ 8 Å (6 keV) ~ 50 Å hard x-ray PES (h ~ several keV) Surface versus bulk: V2O3 G. Panaccione et al., PRL 97, 116401 (2006)

  24. h e- • Outline: • Photoemission of interacting electron systems • Mott-Hubbard physics in transition metal oxides • Correlation effects in 1D • TiOCl: Challenges for ab initio many-body theory

  25. k0 k A(k,) k kF Fermi liquid non-interacting electrons dressed quasiparticles bare particles EF=0 energy Spectral function of a Fermi liquid

  26. a = a r(w) ~ w 0.125 density of states spin 0.5 charge spin 1 1.5 E w charge F 2 Electron-electron interaction in 1D metals Tomonaga-Luttinger model: E 0(k) EF k kF Voit (1995) Schönhammer and Meden (1995)

  27. t t -J U Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  28. Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  29. t J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  30. t J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  31. t J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  32. t J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  33. t J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  34. t J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  35. t J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  36. spinon holon J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy 1D atomic (or molecular) chain

  37. J J J Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy

  38. Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy QP in D>1: heavy hole (quasiparticle)

  39. spinon holon Strongly coupled electrons: 1D Hubbard model t – hopping integral U –local Coulomb energy strong coupling U >> t J  t 2/U- magnetic exchange energy in 1D: spin-charge separation

  40. 0 spin energy relative to EF ~O(J) charge ~O(t) spinon holon -kF kF 3kF /2 -/2  0 momentum 1D Hubbard-Model: spectral function A(k,) K. Penc et al. (1996): tJ-modelJ.M.P. Carmelo et al. (2002 / 2003): Bethe ansatzE. Jeckelmann et al. (2003): dynamical DMRG

  41. TTF-TCNQ: An organic 1D metal strongly anisotropic conductivityb/ab/c~1000

  42. TCNQ-band: ARPES versus 1D Hubbard model photoemission model dynamical DMRGE. Jeckelmann et al., PRL 92, 256401 (2004) model parameters forTCNQ band: n = 0.59(<1) U/t = 4.9 t  2tLDA (?) band theory a c b d

  43. TTF-TCNQ: low energy behavior ? ARPES @ kF • Tomonaga-Luttinger model: • power law exponent for 1D Hubbard model: α 1/8 (~0.04) • experiment: α ~ 1  electron-phonon interaction ?  long-range Coulomb interaction ? ~E1/8 Binding energy (eV)

  44.  extended Hubbard model: local spectral function: V induces larger "band width",i.e. mimicks larger t ! also: Maekawa et al, PRB (2006) TCNQ-band: non-local interaction L. Cano-Cortés et al.,Eur. Phys. J. B 56, 173 (2007) on-site Coulomb energy U (screened): 1.7 eV Hubbard model fit of PES data: 1.9 eV BUT: nearest neighbor interaction V: 0.9 eV

  45. ARPES on SrCuO2 1D Hubbard model (n=1) B.J. Kim et al., Nature Physics 2, 397 (2006) H. Benthien and E. Jeckelmann, in Phys. Rev. B 72, 125127 (2005) Spin-charge separation in 1D Mott insulators

  46. h e- • Outline: • Photoemission of interacting electron systems • Mott-Hubbard physics in transition metal oxides • Correlation effects in 1D • TiOCl: Challenges for ab initio many-body theory

  47. (b) (a) c t t´ b a Ti O Cl b a TiOCl: A low-dimensional Mott insulator • configuration: Ti 3d1 • 1e-/atom: Mott insulator • local spin s=1/2

  48. (b) (a) c t t´ b a Ti O Cl b a TiOCl: A low-dimensional Mott insulator • configuration: Ti 3d1 • 1e-/atom: Mott insulator • local spin s=1/2 • frustrated magnetism, resonating valence bond (RVB) physics ? ?

  49. High T Bonner-Fisher behavior characteristic for 1D AF spin ½ chains Low T spin gap formation of spin singlets due to a spin-Peierls transition ? Magnetic susceptibility: 1D physics

  50. TiOCl: Electronic origin of 1D physics band theory (LDA+U): Seidel et al. (2003)Valenti et al. (2004)

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