講演情報
[14p-K505-4]Numerical calculation of topological invariants in non-Hermitian photonic crystals
〇ThanhHuyen Phan1, Katsunori Wakabayashi1 (1.Kwansei Gakuin Univ.)
キーワード：
photonic crystals、non-Hermition photonics
The topologically protected states in photonic systems have been identified via the property of the band inversion and the localization of electromagnetic waves at edges or interfaces. The calculation of topological invariants such as the Zak phase, which is well-known in Hermitian systems, present new challenges when applied to the non-Hermitian operators. This is especially true if the eigenstates are only accessible through numerical methods. Indeed, several calculations have been done for the Hermitian systems which are analytically available, there is a limit number of studies focusing on the non-Hermitian systems.In this work, we propose a numerical calculation method for the topological invariants, which is based on the Wilson loop. To obtain the smooth results, we introduce the gauge fixing procedure, which contains two parts. First, the arbitrary global phase, which is unavoidably added to each eigenstate at each point in parameter space, are removed by considering consecutive calculation steps. Then, the phase difference between the left and right eigenvectors has to be corrected. We apply this method to calculate the Zak phase and Chern number of non-Hermitian photonic crystals. The non-trivial Zak phase or non-zero Chern number is responsible for the emergence of the edge states.