Electronic excitations in $\gamma$-Li$_2$IrO$_3$

We investigate the electronic properties of the three-dimensional stripyhoneycomb $\gamma$-Li$_2$IrO$_3$ via relativistic density functional theory calculations as well as exact diagonalization of finite clusters and explore the details of the optical conductivity. Our analysis of this quantity reveals the microscopic origin of the experimentally observed (i) optical transitions and (ii) anisotropic behavior along the various polarization directions. In particular we find that the optical excitations are overall dominated by transitions between $j_\text{eff}$ = 1/2 and 3/2 states and the weight of transitions between $j_\text{eff}$ = 1/2 states at low frequencies can be correlated to deviations from a pure Kitaev description. We furthermore reanalyze within this approach the electronic excitations in the known two-dimensional honeycomb systems $\alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$ and discuss the results in comparison to $\gamma$-Li$_2$IrO$_3$.