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Abstract

Two kinds of two-dimensional photonic crystal with hexagonal honeycomb lattices are constructed in which the scatterer and the matrix materials are reversed. Due to the symmetry of special point group, the lattices have p and d orbitals in the center of Brillouin region, which are similar to those in the electronic system. With the structure reversal, the p and d orbitals are also directly inverted. Quantitative analysis shows that the orbital inversion is due to the inversion of air band and medium band because of the local resonance effect in the low frequency bands. Based on the parity properties of p and d orbitals, the pseudo spin states are constructed by analogy to the quantum spin Hall effect in electronic systems. The analysis of the effective Hamiltonian at Γpoint shows that the topological phase transition caused by orbital inversion is revealed. The pseudo spin edge states construct an optimal structure. The electromagnetic wave simulations and energy flow vector analysis show that the structure edge takes on the properties of quantum spin Hall effect, namely, the propagation direction is locked by the spin direction and the propagation is topologically protected. The results also show that the quantum spin Hall effect can be realized without undergoing the closing of gap. The comparison among similar researches indicates that the realization of the pseudo spin states does not need the deformation of lattice, and the structure proposed in this work possesses the characteristics of simple design, wide band gap and strong edge localization.

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Corresponding author:Fang Yun-Tuan,fang_yt1965@sina.com

Funds:Project supported by the Open Fund of Jiangsu Key Laboratory of Security Tech. for Industrial Cyberspace, China (Grant No. STICB201906)

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	p orbit	d orbit
Type A	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {9.8962 \times { {10}^{ - 13} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {6.4143 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.01542\end{array}$	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {2.834 \times { {10}^{ - 12} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {5.9366 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.04774\end{array}$
Type D	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {3.2652 \times { {10}^{ - 12} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {9.2058 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.03574\end{array}$	$\begin{array}{l}\dfrac{ { { {\bar w}_{ {\rm{air} } } } } }{ { { {\bar w}_{ {\rm{dielectric} } } } } } = \dfrac{ {3.603 \times { {10}^{ - 12} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } }{ {8.5597 \times { {10}^{ - 11} }\, {\rm{J} } \cdot { {\rm{m} }^{ - 2} } } } = 0.042\end{array}$

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Vol. 69, Issue 18 - 2020-09-20

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