Spin-orbit-induced exotic insulators in a three-orbital Hubbard model with(t2g)5electrons

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. In these materials, along with moderate electron correlations [6,7], there exists a strong relativistic spin-orbit coupling (SOC), which splits t 2g orbitals, already separated from e g orbitals due to a large crystal field, into the effective total angular momentum j = 1/2 doublet and j = 3/2 quartet orbitals in the atomic limit [8]. Since there are nominally five 5d electrons per Ir ion, the j = 1/2 orbital is half filled while the j = 3/2 orbitals are fully occupied.As opposed to simple expectation from strongly correlated 3d and 4d transition metal oxides [9][10][11][12][13], the experiments have revealed that the ground state of these Ir oxides is a j = 1/2 antiferromagnetic (AF) insulator [14][15][16][17]. The theoretical understanding of the j = 1/2 AF insulator has been also reported [14,[18][19][20][21][22][23][24]. Moreover, even possible unconventional superconductivity has been proposed once mobile carriers are introduced into the insulating state [25][26][27][28]. However, the electronic structure in multi-orbital systems with the competition between the electron correlations and the SOC has not been thoroughly understood. When the SOC is significantly large, the j = 1/2 based band is completely separated from the j = 3/2 based bands, and thus a single-orbital description of the j = 1/2 based band is expected to be valid. On the other hand, when the SOC is small, this picture breaks down and the electronic structure should be largely affected not only by Coulomb interactions but also by the multi-orbital nature. Therefore, a question naturally arises: what is the ground state of multi-orbital systems with the competition between the electron correlations and th...

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