First-principles Simulation of Topological Edge States in Mo2HfC2O2 Nanoribbons

By constructing a multi-orbital tight-binding model using a minimal basis of maximally localized Wannier functions (MLWFs) generated from first-principles electronic band structures, we obtained the electronic band structures of semi-infinite Mo 2 HfC 2 O 2 nanoribbons with a width on the order of 10 nm with minimal computational cost.In this study, we devised Mo 2 HfC 2 O 2 nanoribbon models, where their edge-termination structures are precisely symmetric, and our results have highlighted that variations in edge terminations of the nanoribbon models significantly alter their band structures.In particular, we successfully demonstrated that the energy bands of our models are degenerate at all reciprocal lattice space coordinates along the longitudinal direction of the nanoribbons within the first Brillouin zone, and that the opposite sign of the crystal momentum is accurately reflected in the wave function coefficients of MLWFs.This proves the effectiveness and usefulness of the tight-binding approximation using MLWFs for describing the electronic states of wide nanoribbons.