While the methodology of band structure unfolding has appeared in several publications, the original derivations of the unfolding formulas can be considerably simplified by using the $k$-projection method. In this work, more transparent derivations of unfolded spectral weights are given by using the projection operator approach. A range of illustrative examples are also presented which include finite and random one-dimensional chains, and Kekul\'e-textured honeycomb lattice.
Categories: cond-mat.mtrl-sci cond-mat.dis-nn