Effective theory of quadratic degeneracies
Date of Issue2008
School of Physical and Mathematical Sciences
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.
Physical review B
© 2008 The American Physical Society. This paper was published in Physical Review B and is made available as an electronic reprint (preprint) with permission of The American Physical Society. The paper can be found at the following official DOI: http://dx.doi.org/10.1103/PhysRevB.77.235125. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.