${\mathrm{Na}}_2{\mathrm{IrO}}_3$ as a Novel Relativistic Mott Insulator with a 340-meV Gap

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

Figure 1

(a) Angle-integrated O and Ir valence-band photoemission spectrum of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$; the grey portion is shown in detail in (b)–(d). (b) ARPES EDCs for the Ir $5d$-$t_{2g}$ bands from along $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}K$. (c) Negative second derivative of the ARPES map highlighting the experimental dispersion; superimposed (black diamonds) are the fit analysis results from (d). (d) Model fit of the $\Gamma$-point EDC with 4 Gaussian peaks for the Ir VBs and a Shirley background [23]: 4 peaks are necessary to fit the data set over the full momentum range [matching the number of DOS features from DFT in Figs. 4e, 4f], with Gaussian line shapes yielding better agreement than Lorentzians. The average over $M-\Gamma -K$ gives ($E_{\mathrm{VB}}$, ${\Gamma }_{\mathrm{VB}}$, $\Delta E_{\mathrm{VB}}$) in eV, for peaks 1 to 4: (0.50, 0.30, 0.06); (0.94, 0.39, 0.08); (1.39, 0.44, 0.09); (1.89, 0.43, 0.07).

Figure 2

(a) Background-subtracted angle-integrated EDCs for selected values of K-exposure [see colored markers in (c)]; the chemical potential shift $\Delta \mu$ is revealed by the motion of the high binding-energy trailing edge. (b) Same as in (a), but shifted by the corresponding $\Delta \mu$. (c) $\Delta \mu$ versus the $\mathrm{K}$-deposition time for two different samples; in the inset, $\mathrm{K}$-induced low-energy spectral weight $\Delta \mathrm{SW}$ as a function of $\Delta \mu$, for Sample 2 only. In panel (c) data and error bars are estimated from the comprehensive analysis of both O and Ir trailing edges and peak positions [21]; also note that blue and red curves in (c) and its inset are both a guide-to-the-eye.

Figure 3

Optical conductivity data (red line), together with the simulated Ir $5d$-$t_{2g}$ joint particle-hole DOS (black line), and its individual components from the simultaneous fit of ARPES and optical data [colors and labels are consistent with the valence band features in Fig. 1c, which represent the initial states of the lowest-energy optical transitions]. Inset: Temperature dependence of the gap edge.

Figure 4

(a)–(c) Ir $5d$ $t_{2g}$ band structure ($k_z=0$), and (d)–(f) corresponding DOS, obtained with LDA, $\mathrm{LDA}+\mathrm{SO}$, and $\mathrm{LDA}+\mathrm{SO}+U$ ($U=3\mathrm{eV}$, $J_H=0.6\mathrm{eV}$ [38]). (g) $k_z$ dispersion for the last occupied and first unoccupied Ir $5d$-$t_{2g}$ bands from $\mathrm{LDA}+\mathrm{SO}$, as indicated by the filled region between the $k_z=0$ and $\pi /c$ extreme lines. While the filled areas overlap, resulting in a vanishing indirect gap (i.e., $\Delta k\ne 0$), the direct gap (i.e., $\Delta k=0$) between valence and conduction bands is finite for all $k_z$ and $k_{\parallel }$. (h) $\mathrm{LDA}+\mathrm{SO}$ direct gap distribution along $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}K$, for different $k_z$ in the 3-dimensional Brillouin zone.