Role of basis sets on the unfolding of supercell band structures: From tight-binding to density functional theory

We develop a simple and fast procedure that unfolds band structures obtained from supercell calculations and which is valid for methods based on the linear combination of atomic orbitals, regardless of basis orthogonality. We show that by appropriately choosing the localized basis set, the unfolding formula reduces to a product of selective sums between expansion coefficients. The approach can be directly applied to supercells without the creation of virtual crystals, while it can be further simplified when working directly on the primitive Brillouin zone. Density functional theory examples are given for both ideal and defected systems.