## Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials

Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one of the most actively studied subjects in condensed matter physics, as correlations and SOC together can lead to the discovery of new phases. Examples include unconventional magnetism, spin liquids, and strongly correlated topological phases such as topological superconductivity. Among candidate materials, iridium oxides (iridates) have been an excellent playground to uncover such novel phenomena. In this review, we discuss recent progress in iridates and related materials, focusing on the basic concepts, relevant microscopic Hamiltonians, and unusual properties of iridates in perovskite- and honeycomb-based structures. Perspectives on SOC and correlation physics beyond iridates are also discussed.

Jeffrey G. Rau, Eric Kin-Ho Lee, Hae-Young Kee

## Topological crystalline metal in orthorhombic perovskite iridates

Since topological insulators were theoretically predicted and experimentally observed in semiconductors with strong spin–orbit coupling, increasing attention has been drawn to topological materials that host exotic surface states. These surface excitations are stable against perturbations since they are protected by global or spatial/lattice symmetries. Following the success in achieving various topological insulators, a tempting challenge now is to search for metallic materials with novel topological properties. Here we predict that orthorhombic perovskite iridates realize a new class of metals dubbed topological crystalline metals, which support zero-energy surface states protected by certain lattice symmetry. These surface states can be probed by photoemission and tunnelling experiments. Furthermore, we show that by applying magnetic fields, the topological crystalline metal can be driven into other topological metallic phases, with different topological properties and surface states.

Yige Chen, Yuan-Ming Lu, Hae-Young Kee

## Odd-Parity Triplet Superconducting Phase in Multiorbital Materials with a Strong Spin-Orbit Coupling: Application to Doped Sr2IrO4

We explore possible superconducting states in t2g multiorbital correlated electron systems with strong spin-orbit coupling (SOC). In order to study such systems in a controlled manner, we employ large-scale dynamical mean-field theory (DMFT) simulations with the hybridization expansion continuous-time quantum Monte Carlo (CTQMC) impurity solver. To determine the pairing symmetry, we go beyond the local DMFT formalism using parquet equations to introduce the momentum dependence in the two-particle vertex and correlation functions. In the strong SOC limit, a singlet, d-wave pairing state in the electron-doped side of the phase diagram is observed at weak Hund’s coupling, which is triggered by antiferromagnetic fluctuations. When the Hund’s coupling is comparable to SOC, a twofold degenerate, triplet p-wave pairing state with relatively high transition temperature emerges in the hole-doped side of the phase diagram, which is associated with enhanced charge fluctuations. Experimental implications to doped Sr2IrO4 are discussed.

Zi Yang Meng, Yong Baek Kim, Hae-Young Kee