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We investigate the parity-time (PT) phase transition in photonic crystals with    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$C_{6v}$$\end{document}    C   6  vsymmetry, 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    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$C_{6v}$$\end{document}    C   6  vsymmetry 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.

Parity-time phase transition in photonic crystals with $$C_{6v}$$ symmetry