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arXiv · 0803.1854

Effective theory of quadratic degeneracies

Y. D. Chong·Xiao-Gang Wen·Marin Soljacic
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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.

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Y. D. Chong, Xiao-Gang Wen, Marin Soljacic. 2008-05-06. Effective theory of quadratic degeneracies. https://doi.org/10.1103/physrevb.77.235125

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