Topological Phases of Photonic Crystals under Crystalline Symmetries

TL;DR

This paper provides a comprehensive classification scheme for topological phases in one- and two-dimensional photonic crystals, leveraging symmetry representations to facilitate the design and diagnosis of various topological states.

Contribution

It introduces a symmetry-based classification method for topological bands in photonic crystals, covering phases with and without time-reversal symmetry, including Dirac points and Chern numbers.

Findings

Classified topological bands in 1D and 2D photonic crystals.

Enabled design of topological photonic crystals using symmetry representations.

Diagnosed photonic analogs of obstructed atomic limits and fragile phases.

Abstract

Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological bands in one- and two dimensional photonic crystals, with and without time-reversal symmetry. Our approach exploits the symmetry representations of field eigenmodes at high-symmetry points in momentum space, allowing for the efficient design of a wide range of topological PhCs. In particular, we show that the complete classification provided here is useful for diagnosing photonic crystal analogs of obstructed atomic limits, fragile phases, and stable topological phases that include bands with Dirac points and Chern numbers.