Unidirectional Invisibility and PT-Symmetry with Graphene

We investigate the reflectionlessness and invisibility properties in the transverse electric (TE) mode solution of a linear homogeneous optical system which comprises the $\mathcal{PT}$-symmetric structures covered by graphene sheets. We derive analytic expressions, indicate roles of each parameter governing optical system with graphene and justify that optimal conditions of these parameters give rise to broadband and wide angle invisibility. Presence of graphene turns out to shift the invisible wavelength range and to reduce the required gain amount considerably, based on its chemical potential and temperature. We substantiate that our results yield broadband reflectionless and invisible configurations for realistic materials of small refractive indices, usually around $\eta = 1$, and of small thickness sizes with graphene sheets of rather small temperatures and chemical potentials. Finally, we demonstrate that pure $\mathcal{PT}$-symmetric graphene yields invisibility at small temperatures and chemical potentials.Comment: 20 pages, 1 table 17 figure

Broadband and Wide-Angle Invisibility with PT-Symmetric 2D-Weyl Semimetal

Inspired by the magnificent features of two-dimensional (2D) materials which aroused much of the interest in recent materials science research, we study PT-symmetric 2D Weyl semimetal (WSM) to reveal the broadband and wide-angle invisible configurations in a PT-symmetric optical slab system. Desired unidirectional reflectionlessness and invisibility phenomena is obtained by the optimal control of system parameters. We unravel the mystery of broadband and wide-angle invisibility in regular slab materials with finite refractive indices by means of the plenary expressions. We show that materials whose refractive indices relatively small (usually around $\eta =1$) give rise to quite a lot broadband and wide-angle (almost all incidence angles) invisible configurations. This is not observed with any 2D material other than 2D WSMs. Our findings suggest a concrete expedience to experimental realizations in this direction.Comment: 8 pages, 11 figure

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page