Optical $N$insulators: topological obstructions in the atomistic susceptibility tensor
Abstract
A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational symmetry in both directions. Similarly, Wannier functions that respect timereversal symmetry cannot be formed in quantum spin Hall insulators. This molecular orbital interpretation of topology has been enlightening and was recently extended to topological crystalline insulators which include obstructions tied to space group symmetries. In this article, we introduce a new class of twodimensional topological materials known as optical $N$insulators that possess obstructions to constructing localized molecular polarizabilities. The optical $N$invariant $N\in\mathbb{Z}$ is the winding number of the atomistic susceptibility tensor $\chi$ and counts the number of singularities in the electromagnetic linear response theory. We decipher these singularities by analyzing the optical band structure of the material  the eigenvectors of the susceptibility tensor  which constitutes the collection of optical Bloch functions. The localized basis of these eigenvectors are optical Wannier functions which represent the molecular polarizabilities at different lattice sites. We prove that in a nontrivial optical phase $N\neq 0$, such a localized polarization basis is impossible to construct. Utilizing the mathematical machinery of $K$theory, these optical $N$phases are refined further to account for the underlying crystalline symmetries of the material, generating a classification of the topological electromagnetic phase of matter.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10595
 Bibcode:
 2021arXiv211010595V
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Materials Science
 EPrint:
 14 pages, 3 figures