TransversalityEnforced TightBinding Model for 3D Photonic Crystals aided by Topological Quantum Chemistry
Abstract
Tightbinding models can accurately predict the band structure and topology of crystalline systems and they have been heavily used in solidstate physics due to their versatility and low computational cost. It is quite straightforward to build an accurate tightbinding model of any crystalline system using the maximally localized Wannier functions of the crystal as a basis. In 1D and 2D photonic crystals, it is possible to express the wave equation as two decoupled scalar eigenproblems where finding a basis of maximally localized Wannier functions is feasible using standard Wannierization methods. Unfortunately, in 3D photonic crystals, the vectorial nature of the electromagnetic solutions cannot be avoided. This precludes the construction of a basis of maximally localized Wannier functions via usual techniques. In this work, we show how to overcome this problem by using topological quantum chemistry which will allow us to express the band structure of the photonic crystal as a difference of elementary band representations. This can be achieved by the introduction of a set of auxiliary modes, as recently proposed by Soljačić et. al., which regularize the $\Gamma$point obstruction arising from transversality constraint of the Maxwell equations. The decomposition into elementary band representations allows us to isolate a set of pseudoorbitals that permit us to construct an accurate transversalityenforced tightbinding model (TETB) that matches the dispersion, symmetry content, and topology of the 3D photonic crystal under study. Moreover, we show how to introduce the effects of a gyrotropic bias in the framework, modeled via nonminimal coupling to a static magnetic field. Our work provides the first systematic method to analytically model the photonic bands of the lowest transverse modes over the entire BZ via a TETB model.
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.18257
 arXiv:
 arXiv:2305.18257
 Bibcode:
 2023arXiv230518257M
 Keywords:

 Physics  Optics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Physics  Applied Physics
 EPrint:
 3 figures