Unfolding method for band structures

When the band structure of a system with imperfection such as surfaces, impurities, vacancies, and structural distortion calculated by the supercell approach is compared to spectrum measured by Angle-Resolved Photoemission Spectroscopy (ARPES), the experimentally measured periodicity of the system is generally different from that of the supercell we introduced for the calculation. In such a case, the band structure obtained by the supercell calculation should be represented for the Brillouin zone of a proper unit cell so that the periodicity of calculated band structure can be consistent with the measured one. Though the choice of the proper unit cell is not obvious in general cases, OpenMX provides a method for unfolding the band structure of the supercell into the Brillouin zone of a reference unit cell that a user specifies in the input file [98]. The functionality is supported for not only collinear, but also non-collinear DFT calculations. Even in case that you are not interested in comparison between calculations and experiments by unfolding the band structrue, the method would be useful to analyze how each band consists of pseudo-atomic orbitals, providing information for physical nature of bands, and how each band is pertubed by the introduced imperfection.

In the following subsequent subsections we explain how these functionalities can be utilized by demonstrating a series of calculations.