Research case study: Direct observation of topologically protected modes in a microwave metamaterial

This year I worked on a project with our collaborators in Birmingham on a very interesting kind of metamaterial. We created a material that supports an electromagnetic wave that can travel in only one direction - the wave is topologically protected. This is useful for communication networks, as when a wave of this kind travels around a corner, or over a defect, it won't be scattered backwards, so there is no loss of signal. Instead of working at the infra-red wavelengths used in communications, we worked at GHz frequencies, where the wavelength is slightly longer (around 3mm) and the materials easier to build.

The metamaterial has a tri-layer unit cell, shown in figure 1A. The top layer is a copper helix embedded in a piece of circuit board. This is chiral, and so breaks the inversion symmetry in the metamaterial. The next layer is a long copper wire on a circuit board, which makes the metamaterial hyperbolic (the dispersion curves extend to infinity, rather than forming a closed loop).

The crosses on these wires are there simply to adjust the capacitance between neighbouring wires. The bottom layer is plain circuit board to prevent electric connection between layers. The unit cell is repeated in three dimensions to make a bulk material.

As the metamaterial is chiral and hyperbolic, the dispersion curve shows Weyl points. These are the 3D version of Dirac points, as seen in the dispersion of graphene. These Weyl points are always present in pairs of opposite chirality, and lead to the presence of surface modes that have different topological charges. A wave that exists on one surface mode cannot jump into the other, and so cannot travel in the opposite direction. 

If we look at the dispersion plot in figure 1B we see solid white lines that represent the modes in the bulk material, and dotted blue lines that represent the topologically protected surface modes. The experimental data was collected in Exeter using a near-field scanning technique, and analysed to show the experimental dispersion.

We were also able to directly image a wave travelling over a sharp corner in the experiment (shown in figure 1C), proving that the wave is indeed topologically protected. This was the first time that these surface modes have been directly imaged in an experiment, and it was a very exciting project to be involved in. ‌

Figure A. Schematic of the unit cell of the 3-dimensional metamaterial showing the helix (chiral) and wire (hyperbolic) components.

Figure B. Dispersion diagram with simulated bulk (solid white) and topologically protected surface (blue dotted) modes, and experimental results (colour plot).

Figure C. Experimental measurement of a surface wave travelling over a sharp step in the material without scattering backwards.