Topological Invariants in Point Group Symmetric Photonic Topological Insulators

TL;DR

This paper introduces a group-theory approach to calculate topological invariants in symmetric photonic crystals, linking symmetry properties to topological phases and enabling rational design of photonic topological states.

Contribution

It presents a novel method using group theory to evaluate topological invariants in bi-isotropic photonic crystals with point group symmetry, connecting symmetry to topological properties.

Findings

Spin Chern number can be evaluated from rotation eigenvalues at high symmetry points.

Topological edge states and band gaps are predicted by total spin Chern number.

Nontrivial phase transitions occur with large magnetoelectric coupling.

Abstract

We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {\epsilon}/{\mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner.