A symmetry-based approach to reciprocal space path selection in band structure calculations

The calculation of band structures is a critical step in describing many different properties of crystalline solids such as optical absorption, and both thermal and electronic transport. Most commonly, these are computed along a one-dimensional path in reciprocal space, which is presumed to capture important features of the entire dispersion landscape. However, conventions for choosing this path rely on data for high-symmetry points and lines in the first Brillouin zone, defined using different arbitrary criteria and an inflexible predefined unit cell. Furthermore, this data is contained in hard-coded lookup tables for different crystal classes and lattice vector lengths. To address these issues, a new “on-the-fly” symmetry based algorithm and utility for obtaining paths in reciprocal space is presented. For an arbitrary input cell, the site-symmetries of points and lines in the first Brillouin zone are determined and used to define the high-symmetry criteria. A smooth path connecting them is then obtained using graph theory based tools. This new framework not only allows for increased flexibility, but is also shown for a general high-symmetry criteria to provide new notable features in the electronic band structure for systems with both magnetic and nonmagnetic symmetry.