It is quite common to perform a supercell calculation for systems containing impurities, vacancies, lattice distortion, or long-range orders, where the translational symmetry is broken. The imperfections not only change the band structures of the original systems but also introduce a large amount of horizontal-like bands due to the band folding from the larger zones into the smaller supercell zones. How heavily the bands are folded to mess up the original band structures depends on how large the supercells are. Of course, the “mess up” also depends on how strong the degree of translational symmetry breaking is. However, the appearance of heavily folded bands is not the case in experimental observations. The measured spectral weight cannot reveal those heavily folded bands even by ideally switching on the small perturbations in their samples. Along this line, most supercell states should carry negligible spectral weight. For having a reasonable comparison with experiments and better visualization to understand symmetry breaking theoretically, I will talk about how to unfold the supercell bands into a larger Brillouin zone.[1, 2] The reference Brillouin zone could be chosen to be larger than the Brillouin zone of the primitive unit cell containing no imperfection. Several examples will be given in the talk. For example, by considering there exists only one lattice in systems like silicene instead of commonly treated two sub-lattices, the two atoms in the primitive unit cell can interfere with each other and cancel the spectral weight in some region in the reciprocal space. The choice of one-Si-atom Brillouin zone can demonstrate good agreement of spectral weight with the ARPES measurement in the case of silicene on ZrB₂ thin film.[3] [1] Wei Ku et al., Phys. Rev. Lett. 104, 216401 (2010).
[2] Chi-Cheng Lee et al., J. Phys.: Condens. Matter 25, 345501 (2013).
[3] Chi-Cheng Lee et al., Phys. Rev. B 90, 075422 (2014).