Effective theory of quadratic degeneracies

• Main Authors: Soljačić, Marin, Chong, Yidong, Wen, Xiao-Gang
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Physics
• Online Access: https://hdl.handle.net/10356/101039; http://hdl.handle.net/10220/18344
• Institution: Nanyang Technological University

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.