Cobaltites
LaCoO3 is a prototypical system with competing spin states. A small gap non-magnetic insulator at low temperature exhibits Curie-Weiss susceptibility above 100 K followed by disappearance of the charge gap between 450 and 600 K. While the low spin (singlet) nature of the ground state is generally accepted, the character of the excited state (intermediate or high spin) is a source of controversy. We have used the LDA+DMFT approach to study the 
thermal and doping effects. Recently, we started to explore the possibility of LaCoO3 being a system close to excitonic condensation. We have found a condensate ground state in Pr0.5Ca0.5CoO3 with LDA+U approach. Treating a simplified model with DMFT we have show the transition in high magnetic field carries characteristics of field-induced excitonic condesation.
Charge transfer materials
Charge-transfer insulators are a subset of strongly correlated (Mott) insulator in which the the charge gap is not defined by the Hubbard bands due to the presence of ligand states (O 2p in oxides). The characteristic feature of charge-transfer insulators is electron-hole asymmetry when it comes to doping. For proper description of charge-transfer materials the p-d hybridization and d-d correlations has to be treated simultaneously (p-d model). We have studied some prototypical charge-transfer materials such as NiO or SrCoO3.
Metal-insulator transition in NiS2-xSex
The NiS2-xSex solid solution provides a model system where the transition between metallic phase and the Mott insulator can be tuned by Se content, pressure or temperature. Using LDA+DMFT we show that, contrary to common claims, the transition is essentially controlled by varying hybridization gap within the S(Se) p-band related to the bond length of the S-S (Se-Se) dimer.
Superconductivity of compressed fcc Li
Discovery of higher temperature superconductivity in MgB2 brought about a renewed interest in strongly coupled conventional superconductors. Surprisingly Li, one of the simplest possible solids, turns out to be ~20 K superconductor when compressed. We use density functional electronic structure and linear response theory to investigate the origin of Li superconductivity and lattice dynamics and to link the effects to the Fermi surface topology.