Quasimolecular electronic structure of Na$_2$IrO$_3$

Spin-orbit (SO) coupling can lead to many nontrivial effects such as Rashba effect, topological insulators, or topologically protected states in systems described the Heisenberg-Kitaev model, recently proposed for Na$_2$IrO$_3$. This proposal is based on the fact the SO coupling for iridium is very strong, and cannot be quenched by the small trigonal crystal field. We show, however, that Na$_2$IrO$_3$ represents a highly unusual case, in which the electronic structure is dominated by the formation of quasi-molecular composite orbitals (QMOs). The QMOs consist of six atomic orbitals on an Ir hexagon, and the orbital moment of each QMO is quenched, so that spin-orbit effects only affect the inter-QMO interaction. The concept of such composite orbitals in solids is completely new, and invokes very different physics compared to the models considered previously. For instance, one has to account for Hubbard correlations among the QMOs, and not individual atomic orbitals. Both the insulating behavior and the experimentally observed zigzag antiferromagnetism in Na$_2$IrO$_3$ naturally follow from the QMO model.