The effect of collective spin-1 excitations on electronic spectra in high- Tc superconductors

We review recent experimental and theoretical results on the interaction between single-particle excitations and collective spin excitations in the superconducting state of high-Tc cuprates. We concentrate on the traces that sharpen features in the magnetic-excitation spectrum (measured by inelastic neutron scattering) and imprint in the spectra of single-particle excitations (measured, e.g. by angle-resolved photoemission spectroscopy, tunnelling spectroscopy, and indirectly also by optical spectroscopy). The ideal object to obtain a quantitative picture for these interaction effects is a spin-1 excitation around 40 meV, termed ‘resonance mode’. Although the total weight of this spin-1 excitation is small, the confinement of its weight to a rather narrow momentum region around the antiferromagnetic wavevector makes it possible to observe strong self-energy effects in parts of the electronic Brillouin zone. Notably, the sharpness of the magnetic excitation in energy has allowed these self-energy effects to be traced in the single-particle spectrum rather precisely. Namely, the doping and temperature dependence together with the characteristic energy and momentum behaviour of the resonance mode has been used as a tool to examine the corresponding self-energy effects in the dispersion and in the spectral line-shape of the single-particle spectra, and to separate them from similar effects due to the electron–phonon interaction. This leads to the unique possibility to single out the self-energy effects due to the spin–fermion interaction and to directly determine the strength of this interaction in high-Tc cuprate superconductors. The knowledge of this interaction is important for the interpretation of other experimental results as well as for the quest for the still unknown pairing mechanism in these interesting superconducting materials. Contents PAGE 1. Introduction 49 2. Experimental evidence of a sharp collective spin excitation and its coupling tofermions 52  2.1. Inelastic neutron scattering 52   2.1.1. Magnetic coupling 53   2.1.2. The magnetic resonance feature 54   2.1.3. Bilayer effects 56   2.1.4. Temperature dependence 58   2.1.5. Doping dependence 60   2.1.6. Dependence on disorder 60   2.1.7. Isotope effect 62   2.1.8. Dependence on magnetic field 62   2.1.9. The incommensurate part of the spectrum 63   2.1.10. The spin-gap 65   2.1.11. The spin fluctuation continuum 65   2.1.12. Normal state spin susceptibility 66  2.2. Angle-resolved photoemission 67   2.2.1. Fermi surface 67   2.2.2. Normal-state dispersion and the flat-band region 69   2.2.3. MDC and EDC 71   2.2.4. Bilayer splitting 73   2.2.5. Superconducting coherence 74   2.2.6. EDC-derived dispersion anomalies 75   2.2.7. The S-shaped MDC-dispersion anomaly 79   2.2.8. The nodal kink 81   2.2.9. Fermi velocity 82   2.2.10. Spectral line-shape 85   2.2.11. The antinodal quasiparticle peak 87   2.2.12. The spectral dip feature 90   2.2.13. Real part of self-energy: renormalization of dispersion 91   2.2.14. Imaginary part of self-energy: quasiparticle lifetime 96   2.2.15. Isotope effect 100   2.2.16. Relation to pseudogap phase 102  2.3. C-axis tunnelling spectroscopy 103  2.4. Optical spectroscopy 105 3. The collective mode as spin-1 exciton 108  3.1. Theoretical models 108  3.2. Characteristic energies 109  3.3. The resonance mode 112   3.3.1. Development of spin exciton 112   3.3.2. Doping dependence 113   3.3.3 Dependence on disorder. 115   3.3.4. Dependence on magnetic field 115   3.3.5. Even and odd mode in bilayer cuprates 118  3.4. The incommensurate response 118  3.5. Effective low-energy theories 119  3.6. Magnetic coherence in La2−xSr x CuO4 123 4. Coupling of quasiparticles to the magnetic resonance mode 124  4.1. The coupling constant and the weight of the spin resonance 126  4.2. Theoretical model 131   4.2.1. Tight binding fit to normal state dispersion 131   4.2.2. Model spectrum and basic equations 134  4.3. Contribution from the spin fluctuation mode 138   4.3.1. Characteristic electronic scattering processes 139   4.3.2. Electronic self-energy 141   4.3.3. Renormalization function and quasiparticle scattering rate 142   4.3.4. Spectral functions at the M point 144  4.4. Contribution of the spin fluctuation continuum 145  4.5. Renormalization of EDC and MDC dispersions 147  4.6. Bilayer splitting 154  4.7. Tunnelling spectra 161  4.8. Doping dependence 164 5. Discussion of phonon effects 167 6. Open problems 169 7. Conclusions 171 Acknowledgements 173 References 173