Symmetry Assumptions, Kramers?Kronig Transformation and Analytical Continuation in Ab Initio Calculations of Optical Conductivities

The limit of infinite relaxation of the Kubo formula and analytical and numerical properties of the Kramers–Kronig transformation and analytical continuation used in ab initio calculations of the optical conductivity tensor are considered. Essential symmetry assumptions used in magneto optics are pointed out and their validity for some classes of important systems is shown. It is shown that for an energy dependent relaxation time, the optical conductivity can always be calculated with desired numerical accuracy by applying a Kramers–Kronig transformation and analytical continuation to the result obtained in the limit of infinite relaxation time instead of calculating it directly from the Kubo formula with a finite relaxation time. Consequently the difference between the two approaches is reduced to the difference between the Brillouin zone integration techniques.