Intensive studies of the interplay between spin-orbit coupling (SOC) and electronic correlations in transition-metal compounds have recently been undertaken. In particular, $j_{\mathrm{eff}}=1/2$ bands on a honeycomb lattice provide a pathway to realize Kitaev's exactly solvable spin model. However, since current wisdom requires strong atomic SOC to make $j_{\mathrm{eff}}=1/2$ bands, studies have been limited to iridium oxides. Contrary to this expectation, we demonstrate how Kitaev interactions arise in $4d$-orbital honeycomb $\alpha \text{−}{\mathrm{RuCl}}_3$, despite having significantly weaker SOC than the iridium oxides, via assistance from electron correlations. A strong-coupling spin model for these correlation-assisted $j_{\mathrm{eff}}=1/2$ bands is derived, in which large antiferromagnetic Kitaev interactions emerge along with ferromagnetic Heisenberg interactions. Our analyses suggest that the ground state is a zigzag-ordered phase lying close to the antiferromagnetic Kitaev spin liquid. Experimental implications for angle-resolved photoemission spectroscopy, neutron scattering, and optical conductivities are discussed.

The electronic structure of the honeycomb lattice iridates ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and ${\mathrm{Li}}_2{\mathrm{IrO}}_3$ has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split $d\mathrm{\text{−}}d$ excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of $j_{\mathrm{eff}}=3/2$ states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of $j_{\mathrm{eff}}$ physics in $A_2{\mathrm{IrO}}_3$. We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and ${\mathrm{Li}}_2{\mathrm{IrO}}_3$ can be described as spin-orbit Mott insulators, similar to the square lattice iridate ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.

$\alpha {\text{-RuCl}}_3$ has been proposed recently as an excellent playground for exploring Kitaev physics on a two-dimensional (2D) honeycomb lattice. However, structural clarification of the compound has not been completed, which is crucial in understanding the physics of this system. Here, using ab initio electronic structure calculations, we study a full three-dimensional (3D) structure of $\alpha {\text{-RuCl}}_3$, including the effects of spin-orbit coupling (SOC) and electronic correlations. The three major results are as follows: (i) SOC suppresses dimerization of Ru atoms, which exists in other Ru compounds such as isostructural ${\mathrm{Li}}_2{\text{RuO}}_3$, and makes the honeycomb closer to an ideal one. (ii) The nearest-neighbor Kitaev exchange interaction between the $j_{\mathrm{eff}}=1/2$ pseudospin strongly depends on the Ru-Ru distance and the Cl position, originating from the nature of the edge-sharing geometry. (iii) The optimized 3D structure without electronic correlations has $P\overline{3}1m$ space-group symmetry independent of SOC, but including electronic correlation changes the optimized 3D structure to either $C2/m$ or $Cmc{2}_1$ within 0.1 meV per formula unit (f.u.) energy difference. The reported $P{3}_{1}12$ structure is also close in energy. The interlayer spin-exchange coupling is a few percent of the in-plane spin-exchange terms, confirming that $\alpha {\text{-RuCl}}_3$ is close to a 2D system. We further suggest how to increase the Kitaev term via tensile strain, which sheds light in realizing the Kitaev spin-liquid phase in this system.

Mott insulators with strong spin-orbit coupling have been proposed to host unconventional magnetic states, including the Kitaev quantum spin liquid. The $4d$ system $\alpha -{\mathrm{RuCl}}_3$ has recently come into view as a candidate Kitaev system, with evidence for unusual spin excitations in magnetic scattering experiments. We apply a combination of optical spectroscopy and Raman scattering to study the electronic structure of this material. Our measurements reveal a series of orbital excitations involving localized total angular momentum states of the Ru ion, implying that strong spin-orbit coupling and electron-electron interactions coexist in this material. Analysis of these features allows us to estimate the spin-orbit coupling strength, as well as other parameters describing the local electronic structure, revealing a well-defined hierarchy of energy scales within the Ru $d$ states. By comparing our experimental results with density functional theory calculations, we also clarify the overall features of the optical response. Our results demonstrate that $\alpha -{\mathrm{RuCl}}_3$ is an ideal material system to study spin-orbit coupled magnetism on the honeycomb lattice.

We predict a quantum phase transition from normal to topological insulators in the 5d transition metal oxide Na2IrO3, where the transition can be driven by the change of the long-range hopping and trigonal crystal field terms. From the first-principles-derived tight-binding Hamiltonian, we determine the phase boundary through the parity analysis. In addition, our first-principles calculations for Na2IrO3 model structures show that the interlayer distance can be an important parameter for the existence of a three-dimensional strong topological insulator phase. Na2IrO3 is suggested to be a candidate material which can have both a nontrivial topology of bands and strong electron correlations.

Numerous efforts have been devoted to reveal exotic semimetallic phases with topologically nontrivial bulk and/or surface states in materials with strong spin-orbit coupling. In particular, semimetals with nodal line Fermi surface (FS) exhibit novel properties, and searching for candidate materials becomes an interesting research direction. Here we provide a generic condition for a fourfold degenerate nodal line FS in nonsymmorphic crystals with inversion and time-reversal symmetry (TRS). When there are two glide planes or screw axes perpendicular to each other, a pair of Bloch bands related by nonsymmorphic symmetry become degenerate on a Brillouin zone (BZ) boundary. There are two pairs of such bands, and they disperse in a way that the partners of two pairs are exchanged on other BZ boundaries. This enforces a nodal line FS on a BZ boundary plane protected by nonsymmorphic symmetries. When TRS is broken, fourfold degenerate Dirac points or Weyl ring FS could occur depending on a direction of the magnetic field. On a certain surface double helical surface states exist, which become double Fermi arcs as TRS is broken.