Effective theory of quadratic degeneracies

TL;DR

This paper develops an effective theoretical framework for understanding quadratic degeneracies in 2D square lattice photonic crystals, explaining how symmetry breaking influences band structure and edge modes.

Contribution

It introduces a new effective theory for quadratic degeneracies in photonic crystals, linking symmetry properties to bandgap opening and edge mode emergence.

Findings

Theory matches numerical photonic bandstructure calculations.

Symmetry breaking can open bandgaps or split degeneracies.

Parity breaking induces reflection-free edge modes.

Abstract

We present an effective theory for the Bloch functions of a two-dimensional square lattice near a quadratic degeneracy point. The degeneracy is protected by the symmetries of the crystal, and breaking these symmetries can either open a bandgap or split the degeneracy into a pair of linear degeneracies that are continuable to Dirac points. A degeneracy of this type occurs between the second and third TM bands of a photonic crystal formed by a square lattice of dielectric rods. We show that the theory agrees with numerically computed photonic bandstructures, and discuss the resulting insight into the reflection-free edge modes induced by parity breaking.