The emergence of Dirac points in photonic crystals with mirror symmetry.

Wen-Yu He,C T Chan

doi:10.1038/srep08186

Abstract

We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes. The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The Dirac nodes can be unbuckled through breaking the mirror symmetry and a photonic analog of Chern insulator can be achieved through time reversal symmetry breaking. Breaking time reversal symmetry can lead to unidirectional helical edge states and breaking mirror symmetry can reduce the band gap to amplify the finite size effect, providing ways to engineer helical edge states.

Highlights

We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes
We show theoretically that Dirac points can potentially emerge in all photonic crystals with mirror symmetry during the closing of a photonic band gap
As we progressively reduce the dielectric constant, the photonic bands will close as some bands separated by the band gaps will approach and touch each other

Summary

The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry

The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. A photonic Chern ‘‘insulator’’ with two helical edge states is realized due to the breaking of time reversal symmetry (here photonic ‘‘insulator’’ means the propagation of light at a certain frequency range is forbidden by an absolute photonic band gap) Introducing such special artificial structure to this photonic Chern ‘‘insulator’’, the finite size effect[20] is found to be amplified, which suppresses one helical edge state while does not influence the other at specific frequency

Results

Hamiltonian as the following

ÀÀ a kx

Conclusion

Additional information