Symmetry indicators vs. bulk winding numbers of topologically nontrivial bands
Abstract
The symmetryindicators provide valuable information about the topological properties of band structures in real materials. For inversionsymmetric, nonmagnetic materials, the pattern of parity eigenvalues of various Kramersdegenerate bands at the timereversalinvariant momentum points are generally analyzed with the combination of strong $Z_4$, and weak $Z_2$ indices. Can the symmetry indicators identify the tunneling configurations of SU(2) Berry connections or the threedimensional, winding numbers of topologically nontrivial bands? In this work, we perform detailed analytical and numerical calculations on various effective tightbinding models to answer this question. If the parity eigenvalues are regarded as fictitious Ising spins, located at the vertices of Miller hypercube, the strong $Z_4$ index describes the net ferromagnetic moment, which is shown to be inadequate for identifying nontrivial bands, supporting even integer winding numbers. We demonstrate that an antiferromagnetic index, measuring the staggered magnetization can distinguish between bands possessing zero, odd, and even integer winding numbers. The coarsegrained analysis of symmetryindicators is substantiated by computing the change in rotationalsymmetryprotected, quantized Berry flux and Wilson loops along various highsymmetry axes. By simultaneously computing ferromagnetic and antiferromagnetic indices, we categorize various bands of bismuth, antimony, rhombohedral phosphorus, and Bi$_2$Se$_3$.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.06871
 Bibcode:
 2021arXiv210906871T
 Keywords:

 Condensed Matter  Materials Science;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 25 pages, 14 figures