Spin-Charge Separation in 1-D. Spin-Charge Separation in 1-D. Spin-Charge Separation - Experiment. Spin-Charge Separation - Experiment
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1 Spin-Charge Separation in 1-D Lecture: Solvable 1D electron systems, Mott insulator and correlated electron systems in 2D Solid State Spectroscopy Course 25/2/2013 Spin : J Charge : t Decay of a photohole into two topological defects in the 1-D chain : Spinon and Holon Bosonization Spin-Charge Separation in 1-D Single-Particle Picture (Band + SDW) Spin-Charge Separation (Composite Particles) Spin-Charge Separation - Experiment SrCuO 2 v spinon v holon Spin : J Charge : t Decay of a photohole into two topological defects in the 1-D chain : Spinon and Holon A Physically Realizable Situation for Tomonaga-Luttinger Liquids? Spin-Charge Separation - Experiment Spin-Charge Separation - Experiment A 0.5 B Direct observation of spin-charge separation in quasi-1d chains of SrCuO 2! BJ. Kim et al., Nature Physics (2006) Momentum (k ) 3 Holon Spinon 2 1 ak Position (ev) Pea k /2 Momentum (k ) Direct observation of spin-charge separation in quasi-1d chains of SrCuO 2! BJ. Kim et al., Nature Physics (2006) 1
2 Expectation from Conventional Picture Anomalous Single Hole Dispersion for 1D and 2D Cases Kim et al., PRL 77, 4054 (1996) Strongly Correlated Electron Systems Materials with extreme properties Control parameters Bandwidth (U/W) Band filling Dimensionality Ca 2-x Sr x RuO 4 d - f open shells materials U<<W Charge fluct. U>>W Spin fluct. I II IIIb IVb Vb VIb VIIb VIIIb Ib IIb III IV V VI VII 0 H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar Mn K Ca Sc Ti V Cr Fe Co Ni Cu Zn Ga Ge As Se Br Kr Tc Ru RbSr Y Zr NbMo RhPdAgCd In SnSbTe I Xe Cs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac** Rf Db Sg Bh Hs Mt Lanthanides* Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Actinides ** Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr High-Tc Colossal MR Heavy Fermions Mott-Hubbard Kondo Spin-charge order Unconventional Temperature (K) Degrees of freedom Charge / Spin Orbital Lattice Nd 2-x Ce x CuO 4 La 2-x Sr x CuO AF AF Pseudogap 'Normal' Metal Dopant Concentration x Mott Insulators and Mott Transition 1937, Deboer & Verwey, NiO, MnO, CoO 1937, Peierls proposal 1949, 51, 56, Mott 1959, Anderson , Hubbard model ~ Metal Insulator Transition (resistance measurements starts ~1946) High Tc Renewed interest in other transition metal oxides Energy Gap of NiO one of the best studied Mott insulators Sawatzky/Allen 2
3 Cartoon of a Mott Insulator Hubbard Model - One of the simplest many body theoretical models Mott insulator A usual halffilled band of metal Solutions at one and infinite dimension Two Band Hubbard Model Charge Transfer Nature of NiO Gap formed between d 8 L and d 9 Charge Transfer Insulator: Zaanen, Sawatzky, Allen Scheme. (Inprovement also on superexchange picture) Sawatzky - Allen Many-Body Interactions in Cuprates : Strong Correlations Many-Body Interactions in Cuprates One-Electron Prediction : La 2-x Sr x CuO (K) Temperature ( AFI 0.20 Hole Doping (x) Half-filled metal with ~ 3 ev bandwidth Real Situation : Mott insulator with ~ 2 ev gap Studying interactions of many holes with spin, lattice, charge degrees of freedom an intractable theoretical problem... Can we simplify the problem (both experimentally and theoretically?) 3
4 A Single Hole in the Mott Insulator ARPES Studies of the Cuprates ture (K) Temperat AFI Bi 2 Sr 2 CaCu 2 O 8+ Bi 2 Sr 2 CuO 6+ YBa 2 Cu 3 O 7- ARPES on Mott insulator : Reflects dynamics of a single hole! A logical starting point for understanding relevant interactions Hole Doping (x) Phase Diagram of Ca 2-x Na x CuO 2 Cl 2 Band Structure Predictions : Non-Interacting T c,max = 28 x = 0.18 x = 0 : T N = 247 K Y. Kohsaka et al., JACS (2002) Kinetic Energy Only Temperatu ure (K) AFI x = 0.05 : No or Neel order x = 0.10 : T c ~ 13 K x= :T c = 22 K Tetragonal K 2 NiF 4 Structure Undistorted square CuO 2 planes Hole Doping (x) Grown under high pressures (~ 4 GPa) Mott Insulator : Magnetic Interactions A Single Hole in the Mott Insulator KE & Magnetism t-j : t-j
5 Comparison with Fermi Liquid Comparison with Fermi Liquid 2. Gaussian Lineshape 2. Lorentzian (FL) Lineshape Comparison with Fermi Liquid 2. Gaussian Lineshape 2. Lorentzian (FL) Lineshape 3. Separation of from peak 3. Peak approaches ~ 400 mev Kinks in the Dispersion : Coupling to a Mode Ca 1.88 Na 0.12 CuO 2 Cl 2 Energy (ev) Momentum k Electron-Boson Coupling in Cuprates Generic Feature to Cuprates NaCCOC Bi2201 Strong Interactions in the Cuprates KE & Magnetism & Lattice LO Bi2212 K.M. Shen et al., (in preparation); A. Lanzara et al., (Nature 01) Ashcroft & Mermin A.S. Mishchenko & N. Nagaosa (PRL 04); O. Rosch & O. Gunnarsson (cond-mat 04) 5
6 Franck-Condon Effect Comparison with Fermi Liquid H 2 H Gaussian Lineshape 2. Lorentzian (FL) Lineshape 3. Separation of from peak 3. Peak approaches g ~ 10 g << 1 ~ 400 mev D.W. Turner, 1970 QP Equivalent to Franck-Condon broadening Doping Evolution of the Cuprates Chemical Potential Shift : O2p & O2p z Emergence of the Sharp Nodal Quasiparticles Resolving the Long-Standing Controversy over the Doping Evolution of the Chemical Potential Shift into LHB / UHB Midgap States Z.-X. Shen et al., PRB 44, P.G. Steeneken et al., PRL 90, N.P. Armitage et al., PRL 88, Y. Kohsaka et al., JPSJ 72, 1018 J.W. Allen et al., PRL 64, 595 R.O. Anderson et al., PRL 70, 3163 A. Ino et al., PRL 79, 2101 N. Harima et al., PRB 64, Evolution of Low Energy States Evolution of Low Energy States K.M. Shen, et al., PRL 93, (2004) 6
7 Evolution of Low Energy States Anisotropic Interactions : Fermi Surface Momentum Anisotropy? x = Overall spectral intensity increases with doping Spectral weight concentrated along the (0,0)- () line Intensity weak at the antinodes (near zone face) K.M. Shen, et al., PRL 93, (2004) Integrated spectral intensity (E F +/- 10 mev), symmetrized Anisotropic Interactions : Fermi Surface x = 0.12 Underlying Fermi Surface x = 0.05 x = 0.10 x = 0.12 x = 0.05 x = 0.10 x = 0.12 Integrated spectral intensity (E F +/- 10 mev), symmetrized 7
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