Abstract
Recent theoretical developments on topological materials, Möbius nanographite and Möbius conjugated polymers, are reported. (I) In nanographite systems with the Möbius boundary condition, there appears a novel magnetic domain. However, this domain state competes against the helical magnetic states. Total energies of the latter states are always lower than that of the former state. Additionally, the domain wall appears in the charge density wave states. (II) Optical properties of Möbius conjugated polymers are studied. We 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 Möbius boundary from those of the periodic boundary. 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. The polarization dependences of electric field of light can detect whether conjugated polymers have the Möbius boundary or not.
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