Electronic correlations and quantum effects in solids

1. Introduction

General reading: Review from Tremel et al., (Solid State Chemistry) on Metal-Insulator transitions (Mott-Hubbard, CDW, Nesting, correlations,...) (German)

2. Electronic correlations, Mott transition

• Independent electrons
• Excitations of the Fermi ground state
• Fermi liquid
• Tight binding
• Tutorial I: Measuring Fermi surfaces of Ni
• General idea of the Mott transition
• Bandwidth controleld Mott transition
• The example of V2O3
• Photoemmission Spectroscopy and inverse PES
• Link: Review Photoemission Spectroscopy Reinert 2005
• Cluster appoach
• Configuration interaction model
• Tutorial II: PES on Ni
• The example of NiO
• Hubbard model
• One-band Hubbard model
• Which electrons are we talking about?
• Hubbard subbands
• The example of RNiO3
• Mott-Hubbard vs. charge transfer insulators
• Bandwidt-controlled metal-insulator transition
• Zaanen-Sawatzki-Allen Schema
• Link: Zaanen-Sawatzki-Allen, PRL 1985
• Link: Experimental Zaanen-Sawatki-Allen schema: Boquet1996
• Negative CT gap

Advanced further reading: M. Imada, A. Fujimori, Y. Tokura: Metal-Insulator transitions, Rev. Mod. Phys. 70, 1039–1263 (1998)

3. t-J model, kinetic exchange, away from half-filling

• t-J model
• Heisenberg Hamiltonian
• Kinetic exchange
• Hole doping
• Tutorial III: Filling-controlled metal-insulator transition
• Zhang-Rice Singlets
• Advanced reading: Zhang, Rice 1988
• Charge mobility and magnetic order
• Excitations, spin-doublon/spin-holon separation
• Link: A. Rosch: Ist ein See von Fermionen immer eine Fermi-Flüssigkeit?
• Charge doping of a 2D quantum antiferromagnet
• Advanced reading: SC and AFM in cuprates
• Tutorial IV: Spin-charge separation
• Kugel-Khomskii exchange, orbital order
• Double exchange
• Link: C. Zener's initial paper
• Colossal Magnetoresistance effect
• Resonant X-ray scattering
• Further reading: P. Abbamonte, Resonant x-ray diffraction demystified
• Link: Resonant scattering beamline at HASYLAB@DESY
• Link: International Workshop on Resonant X-ray Scattering in Electrically-ordered Systems, April 2012

4. Low-dimensional conductors

• Advanced reading: Gruener, Review Mod Phys
• Charge density wave
• Peierls instability
• Link: Peierls Instabilität und Ladungsdichtewellen
• Nesting
• Advanced Reading: Conceptual Aspects of Structure-Property Correlations and
  Electronic Instabilities
• Advanced reading: Schmitt et al.
• Advanced Reading: Brun et al.
• Kohn anomaly
• Advanved reading: Hoesch et al.
• Spin-Peierls transition
• Addendum: Thermopower, transport coefficients

5. Kondo effect, Heavy fermion systems

• Localized magnetic moments in metals
• Kondo effect
• Link: Jun Kondo's homepage
• Kondo resonance
• Heavy fermion systems
• Kondo vs. RKKY
• Doniach diagram
• Mixed valence systems
• Kondo insulators

Advanced reading: P. Coleman, Review 2007