A general group theoretical method to unfold band structures and its application

We present a general method to unfold energy bands of supercell calculations to a primitive Brillouin zone using group theoretical techniques, where an isomorphic factor group is introduced to connect the primitive translation group with the supercell translation group via a direct product. Originating from the translation group symmetry, our method gives a uniform description of unfolding approaches based on various basis sets and therefore should be easy to implement in both tight-binding models and existing ab initio code packages using different basis sets. This makes the method applicable to a variety of problems involving the use of supercells, such as defects, disorder and interfacial reconstructions. As a realistic example, we calculate electronic properties of a monolayer FeSe on SrTiO $_{3}$ in checkerboard and collinear antiferromagnetic spin configurations, illustrating the potential of our method.