First-principle calculation of Chern number in gyrotropic photonic crystals

First-principle calculation of Chern number in gyrotropic photonic crystals

As an important figure of merit for characterizing the quantized collective behaviors of the wavefunction, Chern number is the topological invariant of quantum Hall insulators. Chern number also identifies the topological properties of the photonic topological insulators (PTIs), thus it is of crucia...

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Veröffentlicht in:Optics express 2020-02, Vol.28 (4), p.4638-4649
Hauptverfasser: Zhao, Ran, Xie, Guo-Da, Chen, Menglin L N, Lan, Zhihao, Huang, Zhixiang, Sha, Wei E I
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container_issue 4
container_start_page 4638
container_title Optics express
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creator Zhao, Ran
Xie, Guo-Da
Chen, Menglin L N
Lan, Zhihao
Huang, Zhixiang
Sha, Wei E I
description As an important figure of merit for characterizing the quantized collective behaviors of the wavefunction, Chern number is the topological invariant of quantum Hall insulators. Chern number also identifies the topological properties of the photonic topological insulators (PTIs), thus it is of crucial importance in PTI design. In this paper, we develop a first principle computatioal method for the Chern number of 2D gyrotropic photonic crystals (PCs), starting from the Maxwell's equations. Firstly, we solve the Hermitian generalized eigenvalue equation reformulated from the Maxwell's equations by using the full-wave finite-difference frequency-domain (FDFD) method. Then the Chern number is obtained by calculating the integral of Berry curvature over the first Brillouin zone. Numerical examples of both transverse-electric (TE) and transverse-magnetic (TM) modes are demonstrated, where convergent Chern numbers can be obtained using rather coarse grids, thus validating the efficiency and accuracy of the proposed method.
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title First-principle calculation of Chern number in gyrotropic photonic crystals
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