Spin-orbit-induced exotic insulators in a three-orbital Hubbard model with $(t_{2g})^5$ electrons

TL;DR

This study uses advanced computational methods to explore how spin-orbit coupling induces exotic insulating states, including Mott and excitonic insulators, in a three-orbital Hubbard model with five electrons per site.

Contribution

It demonstrates the importance of basis choice in CTQMC calculations and reveals SOC-driven metal-insulator transitions and excitonic states in a realistic multi-orbital model.

Findings

SOC induces metal-insulator transition at fixed Coulomb interactions.

Antiferromagnetic insulator with $j=1/2$ state for smaller Coulomb interactions.

Emergence of excitonic insulator at larger Coulomb interactions.

Abstract

On the basis of the multi-orbital dynamical mean field theory, a three-orbital Hubbard model with a relativistic spin-orbit coupling (SOC) is studied at five electrons per site. The numerical calculations are performed by employing the continuous-time quantum Monte Carlo (CTQMC) method based on the strong coupling expansion. We find that appropriately choosing bases, i.e., the maximally spin-orbit-entangled bases, drastically improve the sign problem in the CTQMC calculations, which enables us to treat exactly the full Hund's coupling and pair hopping terms. This improvement is also essential to reach at low temperatures for a large SOC region where the SOC most significantly affects the electronic structure. We show that a metal-insulator transition is induced by the SOC for fixed Coulomb interactions. The insulating state for smaller Coulomb interactions is antiferromagnetically ordered with the local effective total angular momentum $j=1/2$, in which the $j=1/2$ based band is essentially half-filled while the $j=3/2$ based bands are completely occupied. More interestingly, for larger Coulomb interactions, we find that an excitonic insulating state emerges, where the condensation of an electron-hole pair in the $j=1/2$ and $j=3/2$ based bands occurs. The origin of the excitonic insulator as well as the experimental implication is discussed.