Tight-binding couplings in microwave artificial graphene

TL;DR

This paper experimentally investigates microwave propagation in an artificial honeycomb lattice, demonstrating tight-binding behavior similar to graphene, and explores how varying resonator spacing affects the density of states and Dirac point energies.

Contribution

It provides experimental validation of tight-binding models in microwave artificial graphene and shows how next-nearest-neighbor couplings influence the density of states.

Findings

Density of states becomes asymmetric with coupling variations

Shift in Dirac point energies observed with lattice modifications

Good agreement with analytical models for infinite lattices

Abstract

We experimentally study the propagation of microwaves in an artificial honeycomb lattice made of dielectric resonators. This evanescent propagation is well described by a tight-binding model, very much like the propagation of electrons in graphene. We measure the density of states, as well as the wave function associated with each eigenfrequency. By changing the distance between the resonators, it is possible to modulate the amplitude of next-(next-)nearest-neighbor hopping parameters and to study their effect on the density of states. The main effect is the density of states becoming dissymmetric and a shift of the energy of the Dirac points. We study the basic elements: An isolated resonator, a two-level system, and a square lattice. Our observations are in good agreement with analytical solutions for corresponding infinite lattice.