Special exceptional point acting as Dirac point in one dimensional PT -symmetric photonic crystal

Abstract

We reveal that a special exceptional point can act as a Dirac point in a one-dimensional PT-symmetric photonic crystal and prove it in detail using our extended first-principle theory. This theory was developed by applying biorthogonal bases of the non-Hermitian Hamiltonian to the kp method to study the dispersion relations of non-Hermitian systems. By using this theory, we demonstrate that two linear dispersions can cross at a critical touching point, which is a special exceptional point, and the corresponding effective Hamiltonian can be cast into a massless Dirac Hamiltonian under the biorthogonal bases of the non-Hermitian Hamiltonian; therefore, this point can be called the Dirac point, and the linear slope can also be predicted. In contrast to the Dirac point in a Hermitian system, which is induced by the degeneracy of two different eigenstates, the Dirac point here is induced by the degeneracy of parallel eigenstates in a non-Hermitian system. In addition, after increasing the non-hermiticity, the Dirac point evolves into a pair of exceptional points, and their positions in the band structure can be predicted well by our theory. Our findings and theory are important for further understanding the physics of the Dirac point in non-Hermitian wave systems.

Recent advances in density functional theory approach for optoelectronics properties of graphene

“…Moreover, despite its high absorption coefficient, one-atom-thick graphene absorbs only 0.023 of visible light and has a reflectance of less than 0.001 of infrared light, according to several experimental findings [ [112] , [113] , [114] ]. This is due to the linear dispersion of the electron, which causes it to behave like a massless material, which is amazing for a monolayer material [ [115] , [116] , [117] ]. However, this is rather poor for applications in photodetection [ 118 , 119 ].…”

Unidirectional and bidirectional photon transport blockade in driven atomic lattices of parity-time antisymmetry

“…The latter indicates that a PT -symmetric optical system must exhibit a delicate balance of gain and loss distributions, corresponding to negative and positive imaginary parts of n(r), respectively. To date, a wide range of extraordinary phenomena, including coherent perfect absorber-laser [3][4][5], power oscillation [2,6,7], single-mode lasing [8][9][10], spatial optical switch [11], and unidirectional invisibility [12][13][14][15][16], have been predicted or observed in PT -symmetric optical platforms, like photonic structures [5,13,[17][18][19][20], waveguides [6-8, 11, 14, 21-23], microcavities [9,10,[24][25][26], and trapped ion systems [27,28].…”

Dirac Points in Chiral Liquid Crystals

“…They are of continuously growing interest for both the fundamental understanding of wave phenomena and its application to photonic devices. Occurrence of exceptional points is another salient example [18][19][20][21][22][23][24][25][26][27]. As mentioned, a Dirac point appears when two bands cross each other locally and exhibit a linear dispersion in any direction in the momentum space.…”