Correlatd electrons: the case of high T c cuprates

Transcription

1 Correlatd electrons: the case of high T c cuprates Introduction: Hubbard U - Mott transition, The cuprates: Band structure and phase diagram NMR as a local magnetic probe Magnetic susceptibilities NMR as a local magnetic probe The single spin fluid ptroblem Hyperfine fields Comparison between different nuclei The pesudogap Questions about the phase diagram

2 Beyond the independent electrons aoproximation LDA: Local interactions between electrons are replaced by an interaction with a potential associated with a mean value of the electronic density. Only valid if the electron kinetic energy is much larger than the interaction between electrons Not good if the electrons are localized in the vicinity of the atomic nucleus LDA narrow band = small kinetic energy

3 Mott Insulators Beyond the LDA Antiferro-magnetic t Hubbard model U Mott Insulating ground state Non doped Cuprates Most simplified model Poorly handled by LDA: Metallic ground state Excited states are not described (transitions between atomic levels) Realistic extension of the LDA: DMFT Atomic state hybridized with a medium with an effective energy spectrum

4 Electronic correlations: Mott -Hubbard metal insulator transition E 0 +U E 0 Set of hydrogen atoms forming a lattice with paramer d One electron per site: atomic level E 0 Coulomb repulsion U forbids double occupancy: excited level E 0 +U d If d decreases U Isolated atoms t INSULATOR W METAL the transfer integral t increases and the band width W increases Insulator to metal transition occurs for U=W U>W gives an insulating magnetic state and not a metallic state for a half filled band

5 SUPERCONDUCTORS Metals and alloys T c Oxides Organic

6 SUPERCONDUCTING CUPRATES La 2 - x Sr x CuO 4 YBa 2 Cu 3 O 6+x

7 PARENT CUPRATES j j < 0 b< < 0 Cu(1) 3d 10 S=0 j < 0 Cu(2) 3d 9 S=1/2

8 Phase Diagram and Band Structure E 3d 10 U 3d 9 O 2p band n(e) E 3d 10 3d 9 O 2p band n(e) Localized Cu holes and Oxygen band carriers? NO!! Strong O2p - Cu 3d hybridization Magnetic correlations

9 Magnetic susceptibilities SQUID Measures χ m ( T ) = = Ion cores orbital Spin χ χ dia dia + + [ ] orb s χ χ ( T ) + + i χ orb χ NMR shift measures on each nuclear site i s + always ( χ imp ) =(x,y,z) i = atomic sites K ( T ) = K dia i + K orb + K s ( T ) = K dia i + A orb χ + orb A s χ s ( T ) Local magnetic measurement on each nuclear site i

10 H.A, T. Ohno and P. Mendels, PRL Y NMR shift CuO 2 plane CuO 2 plane K i dia orb orb s s, ( T ) = K i + Ai, χ + Ai, χ ( T ) Local magnetic measurement But transferred hyperfine couplings

11 Sign if 89 Y NMR shift Negative sign comes from Y4d orbitals: core polarization pπ Y4d pσ Y4d Y4d Y4d Very weak OK So negative sign comes from pσ -Y4d hybridization

12 Is there an independent oxygen band at the Fermi level H.A, T. Ohno and P. Mendels, PRL 1989 K s (ppm) K s (T) = A(4d-2pσ) χ s (T) Slope = A(4d-2pσ) does not change with hole doping So there is no independent oxygen spin degree of freedom at E F

13 Phase Diagram and Band Structure E E 3d 10 3d 10 U 3d 9 O2pσ n(e) O2pσ n(e) 3d 9 WRONG PICTURE Magnetic correlations

14 Zhang-Rice singlet Spin singlets Cu3d O2pσ The holes steal spins from the copper hole background There is a single spin fluid

15 K M. Takigawa et al 1991, 1993 i Single spin fluid behaviour dia orb orb s s, ( T ) = K i + Ai, χ + Ai, χ ( T ) 89 Y versus 17 O 63 Cu versus 17 O A single T dependence for K a (T): due to χ Cu (T) Notice: this allows determinations of the shift references for all nuclei

16 What about the origin of this T dependence? H.A, T. Ohno and P. Mendels, PRL 1989 Origin for K s Large decrease (nearly full loss) of χ s (T) above T c Pseudogap in the electronic excitations

17 H.Alloul, T. Ohno and P. Mendels, PRL 1989 Pseudogap in the cuprates

18 89 Y NMR shift 0.95 T m Phase diagram and pseudogap 0.91 T m Low T decrease of the susceptibility: 0.64 T m opening of the pseudogap 89 K( T ) = σ + A χ( T ) Chemical shift Hyperfine coupling

19 Questions About the Phase Diagram Pseudogap: Phase transition? Crossover? Order parameter? Preformed pairs? M I SG MIT and Disorder? Strange metal? FL Transition to a Fermi liquid? Pseudogap joins Tc curve or QCP??

20 Examples of Magnetic Correlations Magnetic correlations: ZHANG-RICE SINGLET Magnetic correlations and ordered charge segregation: STATIC STRIPES

21 Generic Phase Diagram of the Cuprates? SG This shape of phase diagram is apparently generic However the optimal T c is not generic and the hole concentration is not always well determined