Exciton condensation in bilayer spin-orbit insulator

Nobel phenomena emerging from the cooperation between spin-orbit coupling and electron correlation, such as anomalous magnetoresistance, have caught great attention recently. In particular, 5d orbital electron systems, e.g., strontium iridates and associated thin films, are ideal platforms for studying the complex effect of entangled multiple degrees of freedom. Targetting the bilayer iridate Sr₃Ir₂O₇, we have investigated magnetic excitations of the bilayer Hubbard model in the random phase approximation. We clarified that the electron correlation creates preformed excitons and triggers an exciton Bose-Einstein condensation, which results in the antiferromagnetically ordered state observed in the real material. Here, the spin-orbit coupling induces the quantum critical point at which excitons condense, and the electron correlation drives the system from a paramagnetic band insulator to the Néel phase. Low-energy excitons in the paramagnetic phase re-emerge on the other side of the quantum critical point as the transverse and longitudinal modes of the antiferromagnetic state. A significant softening of the longitudinal mode also occurs in the vicinity of the finite-temperature phase transition point and can be detected in experimental probes, such as resonant inelastic X-ray scattering. These results indicate that the bilayer iridate Sr₃Ir₂O₇ is a realization of the long-sought excitonic insulator. We will show the theoretical calculation of the exciton condensation and discuss possible experimental identification of the antiferromagnetic excitonic insulator.