Projection operator approach to unfolding supercell band structures

TL;DR

This paper introduces a simplified, projection operator-based method for unfolding supercell band structures, providing clearer derivations and illustrative examples across various lattice models.

Contribution

It presents a more transparent derivation of band structure unfolding formulas using the $k$-projection method, improving clarity over previous approaches.

Findings

Simplified derivation of unfolding formulas using projection operators

Application to finite and random 1D chains, and honeycomb lattices

Enhanced understanding of spectral weights in band structure analysis

Abstract

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.