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

TL;DR

This paper reveals that the dispersive Dirac cone, mimicking epsilon-near-zero behavior, is a universal feature in plasmonic crystals with 2D metallic sheets, confirmed through analytical and numerical methods.

Contribution

It introduces a systematic bifurcation approach to demonstrate the universality of Dirac cones in gradient-index plasmonic metamaterials with arbitrary dielectric profiles.

Findings

Analytical derivation of Dirac cone conditions in plasmonic crystals.

Excellent agreement between theory and numerical simulations.

Identification of critical conditions for epsilon-near-zero behavior.

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.