Link to html version of ppt slides for lecture 26.
Reviews:
W. E. Pickett, "Electronic structure of the high-temperature oxide superconductors", Rev. Mod. Phys. 61, 433 (1989).
E. Dagotto, "Correlated Electrons in High Temperature Superconductors",
Rev. Mod. Phys. 66, 763 (1994).
M. Imada, A. Fujimori, and Y. Tokura, "Metal-Insulator Transitions",
Rev. Mod. Phys. 70, 1039 (1998).
A. Damascelli, Z. Hussain, and Z.-X. Shen, "Angle-resolved photoemission studies of the cuprate superconductors",
Rev. Mod. Phys. 75, 473-541 (2003).
- Lattice structures and properties of the CuO materials
- Crystal Structures: CaCuO; La 214; YBa123; (Bi,Tl)Ca 221; (Bi,Tl)BaCa 2212; etc.
- All have same basic CuO2 planes
- Phase diagram as function of "doping"
- Antiferromagnetic (Mott) Insulators (Ideal case!)
- Spin glass (too hard)
- Non-magnetic metal at very high doping (dull)
- Hi-Tc superconductors (mechanism????)
- Independent Electron theory of the CuO materials
- Bands near Fermi energy show which states are relevant
- LDA Fails to describe Mott insulator - apparently very good for doped metal
- Hartree-Fock gives Mott insulator - fails for doped metal (as usual)
- Reminder of what we expect from "Luttinger theorem"
- In AF state (doubled BZ) expect small hole-like Fermi surface if a few (delta) holes are added
- In paramagnetic state expect "large Fermi surface" since there are 1 - delta electrons per cell
- Which is right?
- Experimental evidence indicates large effects of Electron Correlation
- Transport
- Linear resistivity
- Hall effect
- Photoemission
- Shows bands like LDA but reduced weight (renormalized as described by self-energy)
- Sees large Fermi surface, but it is anomalous??
- Attempts to construct realistic theoretical models - How to use LDA in a different way
- Constrained DFT
- Test on Cu atom
- Derivation of parameters in Hubbard model for the solid
- Reduction of atomic-like energies by screening
- Results for Cu O states
- Description of Mott Insulator at half filling
- Cluster Many-body calculation
- Insulating gap
- Superexchange constant in Heisenberg model
- Monte Carlo results imply "large Fermi surface" away from half filling
- But still no evidence of superconductivity in Hubbard Model!
- Conclusions