# Brezels, Bragg & Butterflies: Topological Photonics behind novel broad-band chiro-optical material

Since the award of the 2016 Nobel Prize in Physics for *“theoretical discoveries of topological phase transitions and topological phases of matter”*, topological effects are all the hype in condensed matter physics. In a new paper “Bragg-mirror-like circular dichroism in bio-inspired quadruple-gyroid 4srs nanostructures“, just published by the Nature Group journal *Light: Science & Applications*, we describe the experimental realisation of a photonic material that owes its amazing optical properties to a topological effect.

The material, called 4-srs, is a nanofabricated structure consisting of four entangled highly-periodic networks. Each network is the chiral srs-net, better known as the single gyroid structure. This single network is realised in several butterflies where it acts as a biophotonic crystal. This single gyroid is a chiro-optical material with an ability to discriminate between left- and right-circularly polarised light (Saba et al, 2011; Saba, Wilts et al, 2014) – albeit in a narrow frequency band.

Surprisingly, it is possible to place four copies of this structure -four equal-handed copies of the same network- in space such that they are intertwined without any overlap and still maintain very high (cubic) symmetry. Such space partitions have been explored and described by Stephen Hyde and colleagues (EPL 2000).

When four such structures are intergrown, surprising things happen to the optical properties. Instead of the narrow (and somewhat messy) chiro-optical band structure features of the single srs band structure, a broad-band, highly circular dichroic and very clean band gap result – provided the refractive index is sufficiently high. In fact, the spectral features are reminiscent of the reflectance properties of the so-called Bragg mirror, however with very strong and very broad-band circular dichroism.

What causes the circular dichroism is a topological effect, described by Saba et al, 2011, related to the four-fold intergrowth: The single srs in itself is topologically interesting, as it can be thought of as having the topology of a brezel (when considering its unit cell and periodic gluing) and as it is the simplest graph to span space (de Campo et al 2014).

However, the topological effect that causes the circular dichroic band gap of the 4-srs material is related to the relative arrangement of the 4 networks in space, in particular to the properties of a two-fold screw axis which is simultaneously right- and left-handed. What breaks the symmetry of left-handed and right-handed screw rotations is the fact that for the local network structure around the screw axis (which resembles a double helix) one of transitions is a topologically continuous transition whereas the opposite screw-rotation is topologically discontinuous. This difference leads to difference in left-circularly polarized vs right-circularly polarised reflections off the material.

Visualisations of this difference can be found here: Locally topologically continuous Right-Hand Screw Rotation of double helix structure [symmetry 42(23)] and Locally topologically discontinuous Left-Hand Screw Rotation of double helix structure [symmetry 42(23)].

The 4-srs nanostructure is here realised by a sophisticated 3D Nanoprinting method that can 3D print high-refractive index materials, developed in the group of Min Gu by Ben Cumming and others (Cumming et al 2014, Cumming et al 2011).

The ability to fabricate this fascinating photonic material at technologically relevant wavelengths is an important first step towards possible technological applications. Further, the experimental demonstration of this photonic effect in a nanofabricated material will drive further research aimed at identifying self-assembly strategies for this type of poly-continuous structures.

The full reference for the paper is: Benjamin P Cumming, Gerd E Schröder-Turk, Sukanta Debbarma and Min Gu, “Bragg-mirror-like circular dichroism in bio-inspired quadruple-gyroid 4srs nanostructures”, *Light: Science & Applications* (2017) **6**, e16192; doi:10.1038/lsa.2016.192, Published online 13 January 2017.

(Brezel image from wikimedia under GNU license)