$\mathcal{PT}$-symmetric photonic lattices with type-II Dirac cones

TL;DR

This paper introduces $ ext{PT}$-symmetric photonic lattices with type-II Dirac cones, revealing unique features like the type-II exceptional ring and exploring the effects of non-Hermiticity on beam propagation and symmetry restoration.

Contribution

It is the first demonstration of $ ext{PT}$-symmetric photonic lattices with type-II Dirac cones, linking non-Hermiticity to Lorentz invariance violation in these systems.

Findings

Identification of the type-II exceptional ring.

Restoration of $ ext{PT}$ symmetry by adjusting lattice parameters.

Beam amplitude decay due to diffraction in $ ext{PT}$-symmetric phase, amplification in broken phase.

Abstract

The type-II Dirac cone is a special feature of the band structure, whose Fermi level is represented by a pair of crossing lines. It has been demonstrated that such a structure is useful for investigating topological edge solitons, and more specifically, for mimicking the Kline tunneling. However, it is still not clear what the interplay between type-II Dirac cones and the non-Hermiticity mechanism will result in. Here, this question is addressed; in particular, we report the $\mathcal{PT}$-symmetric photonic lattices with type-II Dirac cones for the first time. We identify a slope-exceptional ring and name it the type-II exceptional ring. We display the restoration of the $\mathcal{PT}$ symmetry of the lattice by reducing the separation between the sites in the unit cell. Curiously, the amplitude of the beam during propagation in the non-Hermitian lattice with $\mathcal{PT}$ symmetry only decays because of diffraction, whereas in the $\mathcal{PT}$ symmetry-broken lattice it will be amplified, even though the beam still diffracts. This work establishes the link between the non-Hermiticity mechanism and the violation of Lorentz invariance in these physical systems.