Kitaev Materials

Simon Trebst

paper

Kitaev Materials

arXiv:1701.07056

Abstract

In transition-metal compounds with partially filled $4 d$ and $5 d$ shells spin-orbit entanglement, electronic correlations, and crystal-field effects conspire to give rise to a variety of novel forms of topological quantum matter. This includes Kitaev materials -- a family of spin-orbit assisted Mott insulators, in which local, spin-orbit entangled $j = 1/2$ moments form that are subject to strong bond-directional interactions. On a conceptual level, Kitaev materials attract much interest for their unconventional forms of magnetism, such as spin liquid physics in two- and three-dimensional lattice geometries or the formation of non-trivial spin textures. Experimentally, a number of Kitaev materials have been synthesized, which includes the honeycomb materials Na $_{2}$ IrO $_{3}$ , $α$ -Li $_{2}$ IrO $_{3}$ , and RuCl $_{3}$ , the triangular materials Ba $_{3}$ Ir $_{x}$ Ti $_{3 - x}$ O $_{9}$ , as well as the three-dimensional hyper-honeycomb and stripy-honeycomb materials $β$ -Li $_{2}$ IrO $_{3}$ and $γ$ -Li $_{2}$ IrO $_{3}$ . These lecture notes provide a short review of the current status of the theoretical and experimental exploration of these Kitaev materials.

24 pages + references, short review for lecture notes of the Julich spring school "Topological Matter" (April 2017)