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

Jason M Munro,Matthew K Horton,Kristin A Persson,Shyam Dwaraknath,Katherine Latimer

doi:10.1038/s41524-020-00383-7

Jason M Munro, Matthew K Horton + Show 3 more

Open Access

https://doi.org/10.1038/s41524-020-00383-7

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Abstract

Band structures for electrons, phonons, and other quasiparticles are often an important aspect of describing the physical properties of periodic solids. Most commonly, energy bands are computed along a one-dimensional path of high-symmetry points and line segments in reciprocal space (the “k-path”), which are assumed to pass through important features of the dispersion landscape. However, existing methods for choosing this path rely on tabulated lists of high-symmetry points and line segments in the first Brillouin zone, determined using different symmetry criteria and unit cell conventions. Here we present a new “on-the-fly” symmetry-based approach to obtaining paths in reciprocal space that attempts to address the previous limitations of these conventions. Given a unit cell of a magnetic or nonmagnetic periodic solid, the site symmetry groups of points and line segments in the irreducible Brillouin zone are obtained from the total space group. The elements in these groups are used alongside general and maximally inclusive high-symmetry criteria to choose segments for the final k-path. A smooth path connecting each segment is obtained using graph theory. This new framework not only allows for increased flexibility and user convenience but also identifies notable overlooked features in certain electronic band structures. In addition, a more intelligent and efficient method for analyzing magnetic materials is also enabled through proper accommodation of magnetic symmetry.

Highlights

Band structures in crystalline solids are of great interest to both experimental and theoretical researchers for their utility in describing a variety of material properties, including well-known phenomena such as optical absorption and thermal and electronic transport, in addition to those of more exotic phases of matter such as topological insulators[1,2,3,4]
Energy bands are computed along high-symmetry line segments in the irreducible Brillouin zone, i.e., the symmetrically unique portion of the minimal unit cell required to describe the crystal in reciprocal space
In 2010, Setyawan and Curtarolo (SC) were the first to propose a standard set of k-paths for each Bravais lattice type with the goal of enabling easy high-throughput calculations of electronic band structures with density functional theory (DFT)[5]

Summary

INTRODUCTION

Band structures in crystalline solids are of great interest to both experimental and theoretical researchers for their utility in describing a variety of material properties, including well-known phenomena such as optical absorption and thermal and electronic transport, in addition to those of more exotic phases of matter such as topological insulators[1,2,3,4]. In 2016 Hinuma et al proposed to alter and expand the scheme to account for the fact that crystals of the same Bravais lattice type could still possess different symmetry in reciprocal space[6] While these works laid an important foundation for k-path selection, and certainly allow for greater consistency across studies, they both identify k-paths in part based on different arbitrary symmetry criteria and unit cell conventions. This new approach does not rely on any a priori cell conventions or hard-coded look-ups Rather, it identifies and selects high-symmetry points and line segments in the Brillouin zone using space group data, in conjunction with very general symmetry criteria. We thereby offer a more accurate treatment of magnetic materials in studies involving band structure calculations

AND DISCUSSION

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