Ab-Initio insight into non-local charge fluctuations in optical conductivity for α-RuCl₃through a Wannier basis: Highlighting the role of chemistry in correlated electron systems

α-RuCl₃ is one of the top contenders for hosting a quantum spin liquid as its exact ground state by possibly being a real material realization of Kitaev's anisotropic spin model. While there is still no consensus for the magnetic ground state, there is plenty of rich physics in the electronic excitations (i.e optical conductivity). We simulate the optical excitations of α-RuCl₃, by invoking a parameter-free treatment of the Random Phase Approximation (RPA) to exact Time Dependent Density Functional Theory (TD-DFT) implemented using a Wannier basis. The calculated optical peak for α-RuCl₃ (peak at ~1eV) is in very good agreement in location and absolute units with experiment. There are two key findings using this implementation. The first is the origin of the insulating gap in the ground state appears to be due to the interplay between relativity (spin-orbit coupling) and correlation (Hubbard U). The second finding is the surprising result that to converge the optical peak in the calculation, there are sizable Ru-Ru electron-hole pairs of Wannier d-like orbitals spanning beyond neighboring sites. This is determined due to the strong covalency built into the underlying solid state electronic structure of the underlying α-RuCl₃, in particular the hexagonal arrangement of Ru atoms.