We investigate the parity-time (PT) phase transition in photonic crystals with [Formula: see text] symmetry, with balanced gain and loss on dielectric rods in the triangular lattice. A two-level non-Hermitian model that incorporates the gain and loss in the tight-binding approximation was employed to describe the dispersion of the PT symmetric system. In the unbroken PT phase, the double Dirac cone feature associated with the [Formula: see text] symmetry is preserved, with a frequency shift of second order due to the presence of gain and loss. The helical edge states with real eigenfrequencies can exist in the common band gap for two topologically distinct lattices. In the broken PT phase, the non-Hermitian perturbation deforms the dispersion by merging the frequency bands into complex conjugate pairs and forming the exceptional contours that feature the PT phase transition. In this situation, the band gap closes and the edge states are mixed with the bulk states.

译文

我们研究了具有 [公式: 参见文本] 对称性的光子晶体中的奇偶时间 (PT) 相变,在三角形晶格中的介电棒上具有平衡的增益和损耗。采用了在紧约束近似中包含增益和损耗的两级非Hermitian模型来描述PT对称系统的色散。在不间断的PT阶段,与 [公式: 参见文本] 对称性相关的双狄拉克锥特征得以保留,由于存在增益和损耗,其频移为二阶。对于两个拓扑上不同的晶格,具有真实本征频率的螺旋边缘状态可以存在于公共带隙中。在中断的PT相位中,非埃尔米特扰动通过将频带合并为复共轭对并形成具有PT相变特征的特殊轮廓来使色散变形。在这种情况下,带隙闭合,边缘状态与体状态混合。

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