Gabriel Kotliar, Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory 14. 10. 06 1/9.

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Presentation transcript:

Gabriel Kotliar, Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory /9

/9 Gabriel Kotliar, Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory

/9 Gabriel Kotliar, Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory

/9 Gabriel Kotliar, Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory

/9 Many 5 d TMOs are metallic. However, there are also some insulating 5 d TMOs : (eg) Sr 2 IrO 4, Sr 3 Ir 2 O 7, BaIrO 3, Y 2 Ir 2 O 7, Eu 2 Ir 2 O 7, Cd 2 Os 2 O 7, Ba 2 NaOsO 6 … 3d3d 4d4d 5d5d (S=1/2) Mott system U (eV)W (eV) 3d TMOs d TMOs d TMOs Bad metal Systematic variations of 3d, 4d and 5d transition metal oxides (TMOs) Oxygen Transition metal oxide In perovskite structure

/9 P. A. Cox, Transition Metal Oxides

/9 P. A. Cox, Transition Metal Oxides

/9 P. A. Cox, Transition Metal Oxides

/9

Schematic representations of the models for strongly correlated electron systems. Left column: Top: Spatial description for the periodic Anderson model, where the hybridization is symbolically shown by thick gray bars. The description for the single-impurity Anderson model, in which only one strongly correlated site hybridized with the itinerant valence bands is considered, is shown in a rectangle. Middle: Spatial Representation for the d-p model, where the single-site cluster model is surrounded by a circle and multi-site cluster model is surrounded by an oval. Bottom: Spatial description for the Hubbard model. Right column: Top: Energy diagrams for the periodic Anderson model. Single-impurity Anderson model is surrounded by a rectangle. Middle: Case for a single-site cluster model. The dashed lines show the correspondence of the ligand levels in the cluster model to the representative discrete levels extracted from the itinerant continuum bands in the single-impurity Anderson model, where both are hybridized with the strongly correlated states. In the right panels showing the energy diagrams, the filled (empty) circles denote the occupied electrons (holes) and the lines between the filled and empty circles represent a charge transfer.