Electronic States and the Anomalous Hall Effect in Strongly Correlated Topological Systems

Elementary excitations, the spin-liquid state, and the anomalous Hall effect, including the quantum Hall effect, are considered in layered strongly correlated systems. The mechanisms of formation of a topological state associated with the bare flat energy bands, correlations, and the spin-orbit interaction, including the appearance of correlated Chern bands, are analyzed. A two-band picture of the spectrum in metallic kagome lattices is proposed, including the transition from a ferromagnetic state, a flat strongly correlated band, and a band of light Dirac electrons. In this case, the effect of separation of spin and charge degrees of freedom turns out to be significant. The application of the Kotliar-Ruckenstein slave-boson and the Ribeiro-Wen dopon representations to this problem is discussed.