Universal behavior of a dispersive Dirac cone in gradient-index plasmonic metamaterials

Matthias Maier, Marios Mattheakis, Efthimios Kaxiras, Mitchell Luskin, and Dionisios Margetis

Phys. Rev. B 97, 035307 – Published 25 January 2018

Abstract

We demonstrate analytically and numerically that the dispersive Dirac cone emulating an epsilon-near-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 transverse-magnetic (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.

Received 7 November 2017

DOI:https://doi.org/10.1103/PhysRevB.97.035307

Physics Subject Headings (PhySH)

Plasmonics

Graphene Metamaterials

Bloch wave theory Numerical techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Matthias Maier^1,*, Marios Mattheakis^2,†, Efthimios Kaxiras^2,3, Mitchell Luskin¹, and Dionisios Margetis⁴

¹School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
²School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
³Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
⁴Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland 20742, USA