Theoretical investigation on electronic properties of topological materials: Optical excitations in Moebius conjugated polymers

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Electronic structures and optical excitations in Moebius conjugated polymers are studied theoretically. Periodic and Moebius boundary conditions are applied to the tight binding model of poly(para-phenylene), taking into account of the exciton effects by long-range Coulomb interactions. We first discuss that oligomers with a few structural units are more effective than polymers, in order to measure effects of discrete wave numbers which are shift by the Moebius boundary from those of the periodic boundary. Next, calculations of the optical absorption spectra are reported. Certain components of the optical absorption for the electric field perpendicular to the polymer axis mix with the absorption spectra for the electric filed parallel with the polymer axis. Therefore, the polarization dependences of electric field of light can detect whether conjugated polymers have the Moebius boundary or not.