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 band gap 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 transverse magnetic bands of a photonic crystal formed by a square lattice of dielectric rods. We show that the theory agrees with numerically computed photonic band structures and yields the correct Chern numbers induced by parity breaking.
- Received 28 March 2008
DOI:https://doi.org/10.1103/PhysRevB.77.235125
©2008 American Physical Society