Abstract
We investigate the parity-time (PT) phase transition in photonic crystals with C_{6v} 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 C_{6v} 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.
Highlights
We investigate the parity-time (PT) phase transition in photonic crystals with C6v symmetry, with balanced gain and loss on dielectric rods in the triangular lattice
The quantum spin Hall (QSH) s tate4–6 belongs to a different topological class that preserves the TR symmetry, in which no magnetic field is required and the spin-orbit interaction is responsible for the topological character
For a triangular lattice composed of dielectric rods, the PT symmetry is established by an antisymmetric arrangement of gain and loss on the rods in the unit cell
Summary
We investigate the parity-time (PT) phase transition in photonic crystals with C6v symmetry, with balanced gain and loss on dielectric rods in the triangular lattice. In the unbroken PT phase, the double Dirac cone feature associated with the C6v symmetry is preserved, with a frequency shift of second order due to the presence of gain and loss. 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. In the dielectric photonic crystals with C6v symmetry, the combinations of doubly degenerate E1 and E2 modes form two pairs of pseudospin states, which are referred to as the p and d orbitals. By judiciously incorporating gain and loss in the system, the non-Hermitian
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