Na$_2$IrO$_3$ as a Novel Relativistic Mott Insulator with a 340\,meV Gap

We have studied Na$_{2}$IrO$_{3}$ by ARPES, optics, and band structure calculations in the local-density approximation (LDA). The weak dispersion of the Ir 5$d$-$t_{2g}$ manifold highlights the importance of structural distortions and spin-orbit coupling (SO) in driving the system closer to a Mott transition. We detected an insulating gap $\Delta_{gap}\!\simeq\!340$\,meV which, at variance with a Slater-type description, is already open at 300\,K and does not show significant temperature dependence even across $T_N\!\simeq\!15$\,K. An LDA analysis with the inclusion of SO and Coulomb repulsion U revealed that, while the prodromes of an underlying insulating state are already found in LDA+SO, the correct gap magnitude can only be reproduced by LDA+SO+U, with $U\!=\!3$\,eV. This establishes Na$_2$IrO$_3$ as a novel type of Mott-like correlated insulator in which Coulomb and relativistic effects have to be treated on an equal footing.