Kitaev quantum spin liquid - concept and materialization

A decade ago, Alexei Kitaev proposed an exactly solvable $S$ = 1/2 model on a two-dimensional honeycomb lattice, where the spins fractionalize into Majorana fermions and form a topological quantum spin liquid (QSL) in the ground state. It was soon recognized that a family of complex iridium oxides, as well as ruthenium chloride, with honeycomb structure are magnetic insulators and accommodate essential ingredients of the Kitaev model, due to the interplay of electron correlation and spin-orbit coupling. This initiated a race to materialize the Kitaev QSL and to capture the signature of Majorana fermions. In this review, we provide a wide perspective of this rapidly growing field, including theory, materials and experiment. We first summarize the theoretical background of the Kitaev QSL ground state and its materialization using spin-orbital-entangled $J_{\rm eff}$ = 1/2 moments. This is followed by an overview of candidate materials and their magnetic properties, including Na$_2$IrO$_3$, $\alpha$, $\beta$, $\gamma$-Li$_2$IrO$_3$,$\alpha$-RuCl$_3$ and H$_3$LiIr$_2$O$_6$. Finally, we review the latest exciting progress in the search for the Kitaev QSL. In particular, H$_3$LiIr$_2$O$_6$ and $\alpha$-RuCl$_3$ in applied magnetic field show signatures of the QSL state, and $\alpha$-RuCl$_3$ has unusual magnetic excitations and thermal transport properties that are consistent with spin fractionalization.