Correlated Quantum Phenomena in the Strong Spin-Orbit Regime

We discuss phenomena arising from the combined influence of electron correlation and spin-orbit coupling (SOC), with an emphasis on emergent quantum phases and transitions in heavy transition metal compounds with 4d and 5d elements. A common theme is the influence of spin-orbital entanglement produced by SOC, which influences the electronic and magnetic structure. In the weak-to-intermediate correlation regime, we show how nontrivial band-like topology leads to a plethora of phases related to topological insulators (TIs). We expound these ideas using the example of pyrochlore iridates, showing how many novel phases, such as the Weyl semimetal, axion insulator, topological Mott insulator, and TIs, may arise in…