Domain Wall in Multimode Peierls State

The domain wall as a one-dimensional discommensuration of the multimode Peierls (MMP) lattice distortion is investigated numerically based on the Su–Schrieffer–Heeger model generalized to the square lattice with the half-filled electronic band. In order to create the domain wall, we consider a spin excitation where the total number of spin-up electrons is larger than that of spin-down electrons by the linear dimension of the square lattice. The extra spins are localized at the domain wall, and the localized wave functions form a mid-gap band with zero energy. The localized wave functions are analytically constructed in the same way as the edge states in the graphene nanoribbon. The properties of the localized states for the domain walls with various orientations to the MMP distortion pattern are elucidated. The number of the zero-energy states for every orientation satisfies the index theorem established in the Dirac electron system. Furthermore, the correlation effects on the domain wall are studied by i...