Concept and realization of Kitaev quantum spin liquids

The Kitaev model is an exactly solvable S = 1/2 spin model on a 2D honeycomb lattice, in which the spins fractionalize into Majorana fermions and form a topological quantum spin liquid (QSL) in the ground state. Several complex iridium oxides, as well as alpha-RuCl3, are magnetic insulators with a honeycomb structure, and it was noticed that they accommodate essential ingredients of the Kitaev model owing to the interplay of electron correlation and spin-orbit coupling. This has led to a race to realize the Kitaev QSL and detect signatures of Majorana fermions. We summarize the theoretical background of the Kitaev QSL ground state and its realization using spin-orbital entangled J(eff) = 1/2 moments. We provide an overview of candidate materials and their electronic and magnetic properties, including Na2IrO3, alpha-Li2IrO3, beta-Li2IrO3, gamma-Li2IrO3, alpha-RuCl3 and H3LiIr2O6. Finally, we discuss experiments showing that H3LiIr2O6 and alpha-RuCl3 in an applied magnetic field exhibit signatures of the QSL state and that alpha-RuCl3 has unusual magnetic excitations and thermal transport properties consistent with spin fractionalization. The Kitaev quantum spin liquid is an exotic phase of matter exhibiting long-range entanglement and emergent Majorana fermions. This Review summarizes the concept and recent progress in realizing Kitaev model physics in transition metal compounds.