The electromagnetic response of a two-dimensional metal embedded in a periodic array of a dielectric host can give rise to a plasmonic Dirac point that emulates epsilon-near-zero (ENZ) behavior. This theoretical result is extremely sensitive to structural features like periodicity of the dielectric medium and thickness imperfections. We propose that such a device can actually be realized by using graphene as the two-dimensional metal and materials like the layered semiconducting transition-metal dichalcogenides or hexagonal boron nitride as the dielectric host. We propose a systematic approach, in terms of design characteristics, for constructing metamaterials with linear, elliptical, and hyperbolic dispersion relations which produce ENZ behavior, normal or negative diffraction. DOI: 10.1103/PhysRevB.94.201404 The confinement of metallic ("free") electrons in twodimensional interfaces can produce powerful effects used to drive electromagnetic (EM) devices like nanoantennas with extremely short wavelength resonance [1,2], metalenses and optical holography [3][4][5], active plasmonic systems [6][7][8], and sub-wavelength Bloch oscillations [9,10]. The key feature for such applications is the creation of waves propagating along a metal-dielectric interface with wavelength shorter than that of the incident radiation, while the waves decay exponentially in the perpendicular direction. This surface effect involves electronic motion (plasmons) coupled with electromagnetic waves (polariton) and is referred to as surface plasmon polariton (SPP). By combining the properties of different materials, it is even possible to produce behavior not found under normal circumstances like negative refraction [11][12][13][14][15][16], epsilon-near-zero (ENZ) [17][18][19], discrete solitons [20,21], and quantum control of light [22,23].The bottleneck in creating SPP devices with any desirable characteristic has been the limitations of typical three-dimensional solids in producing perfect interfaces for the confinement of electrons and the features of dielectric host. This may no longer be a critical issue. The advent of truly two-dimensional (2D) materials like graphene (a metal), transition-metal dichalcogenides (TMDC's, semiconductors), and hexagonal boron nitride (hBN, an insulator) make it possible to produce structures with atomic-level control of features in the direction perpendicular to the stacked layers [24][25][26][27]. This is ushering a new era in manipulating the properties of plasmons and designing devices with extraordinary behavior. In particular, 2D structures support plasmons (collective excitations) which fundamentally differ from SPPs, since the charge carriers are restricted in two dimensions [28,29]. Nevertheless, 2D plasmons and SPPs share similarities in field profiles and in dispersion behavior and could be used * mariosmat@seas.harvard.edu; http://scholar.harvard.edu/marios _matthaiakis/home † konstantinos.valagiannopoulos@nu.edu.kz; https://sst.nu.edu.kz /konstantinos-valagiannopoulos/ interchangeably fo...

We investigate certain configurations of Luneburg lenses that form light propagating and guiding networks. We study single Luneburg lens dynamics and apply the single lens ray tracing solution to various arrangements of multiple lenses. The wave propagating features of the Luneburg lens networks are also verified through direct numerical solutions of Maxwell's equations. We find that Luneburg lenses may form efficient waveguides for light propagation and guiding. The additional presence of nonlinearity improves the focusing characteristics of the networks.

Direct visualization of nanometer-scale properties of moiré superlattices in van der Waals heterostructure devices is a critically needed diagnostic tool for study of the electronic and optical phenomena induced by the periodic variation of atomic structure in these complex systems. Conventional imaging methods are destructive and insensitive to the buried device geometries, preventing practical inspection. Here we report a versatile scanning probe microscopy employing infrared light for imaging moiré superlattices of twisted bilayers graphene encapsulated by hexagonal boron nitride. We map the pattern using the scattering dynamics of phonon polaritons launched in hexagonal boron nitride capping layers via its interaction with the buried moiré superlattices. We explore the origin of the double-line features imaged and show the mechanism of the underlying effective phase change of the phonon polariton reflectance at domain walls. The nano-imaging tool developed provides a non-destructive analytical approach to elucidate the complex physics of moiré engineered heterostructures.

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We demonstrate analytically and numerically that the dispersive Dirac cone emulating an epsilonnear-zero (ENZ) behavior is a universal property within a family of plasmonic crystals consisting of two-dimensional (2D) metals. Our starting point is a periodic array of 2D metallic sheets embedded in an inhomogeneous and anisotropic dielectric host that allows for propagation of transversemagnetic (TM) polarized waves. By invoking a systematic bifurcation argument for arbitrary dielectric profiles in one spatial dimension, we show how TM Bloch waves experience an effective dielectric function that averages out microscopic details of the host medium. The corresponding effective dispersion relation reduces to a Dirac cone when the conductivity of the metallic sheet and the period of the array satisfy a critical condition for ENZ behavior. Our analytical findings are in excellent agreement with numerical simulations.

By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host. This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our findings. In particular, we emphasize the role of the vector-valued corrector field, which expresses microscopic modes of surface waves on the 2D material. We demonstrate how our homogenization procedure may set the foundation for computational investigations of: effective optical responses of reasonably general geometries, and complicated design problems in the plasmonics of 2D materials.

Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two-and few-layer configurations of graphene have been realized and studied, a systematic investigation of the properties of arbitrarily layered graphene assemblies is still lacking. We introduce theoretical concepts and methods for the processing of materials information, and as a case study, apply them to investigate the electronic structure of multi-layer graphene-based assemblies in a high-throughput fashion. We provide a critical discussion of patterns and trends in tight binding band structures and we identify specific layered assemblies using low-dispersion electronic bands as indicators of potentially interesting physics like strongly correlated behavior. A combination of data-driven models for visualization and prediction is used to intelligently explore the materials space. This work more generally aims to increase confidence in the combined use of physics-based and data-driven modeling for the systematic refinement of knowledge about 2D layered materials, with implications for the development of novel quantum devices.

Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations. Two fundamental challenges facing the development of neural networks in physics applications is their lack of interpretability and their physics-agnostic design. The focus of the present work is to embed physical constraints into the structure of the neural network to address the second fundamental challenge. By constraining tunable parameters (such as weights and biases) and adding special layers to the network, the desired constraints are guaranteed to be satisfied without the need for explicit regularization terms. This is demonstrated on supervised and unsupervised networks for two basic symmetries: even/odd symmetry of a function and energy conservation. In the supervised case, the network with embedded constraints is shown to perform well on regression problems while simultaneously obeying the desired constraints whereas a traditional network fits the data but violates the underlying constraints. Finally, a new unsupervised neural network is proposed that guarantees energy conservation through an embedded symplectic structure. The symplectic neural network is used to solve a system of energy-conserving differential equations and outperforms an unsupervised, non-symplectic neural network.