Linear scaling approach for optical excitations using maximally localized Wannier functions

We present a theoretical method for calculating optical absorption spectra based on maximally localized Wannier functions, which is suitable for large periodic systems. For this purpose, we calculate the exciton Hamiltonian, which determines the Bethe-Salpeter equation for the macroscopic polarization function and optical absorption characteristics. The Wannier functions are specific to each material and provide a minimal and therefore computationally convenient basis. Furthermore, their strong localization greatly improves the computational performance in two ways: first, the resulting Hamiltonian becomes very sparse and, second, the electron-hole interaction terms can be evaluated efficiently in real space, where large electron-hole distances are handled by a multipole expansion. For the calculation of optical spectra we employ the sparse exciton Hamiltonian in a time-domain approach, which scales linearly with system size. We demonstrate the method for bulk silicon—one of the most frequently studied benchmark systems—and envision calculating optical properties of systems with much larger and more complex unit cells, which are presently computationally prohibitive.