Impact of structural distortions on the correlated electronic structure of orbital-selective Mott insulating Na$_3$Co$_2$SbO$_6$ under strains

Abstract

Na$_{3}$Co$_{2}$SbO$_6$ is a promising candidate to realize the Kitaev spin liquid phase since the large Kitaev spin exchange interaction is tunable via the change in electronic structure, such as the trigonal crystal field splitting ($\Delta_{TCF}$). Here, we show that the uncorrelated electronic structure of Na$_{3}$Co$_{2}$SbO$_6$ is rather insensitive to the strain effect due to the low crystal symmetry accompanied by oxygen displacements and the presence of Sb $s$ orbitals. This suggests that the Kitaev spin-exchange interaction obtained from perturbation theory also does not depend much on the strain effect. Using density functional theory plus dynamical mean field theory, we find that the correlated electronic structure of Na$_{3}$Co$_{2}$SbO$_6$ is an orbital selective Mott insulating state where the trigonal $a_{1g}$ orbital is insulating due to correlation-assisted hybridization, while other $d$ orbitals behave as typical Mott insulators, resulting in tunability of $\Delta_{TCF}$ under the strain effect effectively. Our results show that the local Co-site symmetry and dynamical correlation effects will play an important role in engineering the novel magnetic phase in this and related materials.