Wannier exciton states in a 1D topological chain

Abstract

This thesis investigates the properties of 1D Wannier excitons in a 1D s-p wave hybrid chain. Based on the tight-binding model, we first calculate the winding number of the single-electron band structure. Then, we introduce the particle-hole basis with the interband Coulomb interaction in 1D to determine the bound-state spectrum and the dispersion relation of excitons. Finally, we calculate the winding number for the exciton states themselves and show that it is exactly twice as large as the single-electron winding number in the same 1D chain.