Thèse du Désordre Structural à l'Ordre Topologique Imagerie 3D des Joints de Grains dans les Cristaux Photoniques Gyroïdes Biologiques H/F - 38

Établissement : Université Grenoble Alpes
École doctorale : PHYS - Physique
Laboratoire de recherche : Modélisation et Exploration des Matériaux
Direction de la thèse : Joël EYMERY ORCID 0000000242161166
Début de la thèse : 2026-10-01
Date limite de candidature : 2026-05-13T23:59:59

Les cristaux photoniques sont des structures diélectriques périodiques qui contrôlent la propagation de la lumière par leur géométrie. Les cristaux photoniques tridimensionnels aux longueurs d'onde visibles présentent un intérêt particulier pour le guidage, le filtrage et la détection de la lumière. Lorsque le réseau d'un tel cristal contient des distorsions structurales brisant sa symétrie interne, la théorie prédit l'émergence d'états topologiques (points de Weyl). Des modes de surface protégés aux interfaces entre domaines peuvent être obtenus avec des propriétés de propagation directionnelle, très utiles à la conception de dispositifs photoniques. Tester ces prédictions nécessite des cristaux photoniques 3D à l'échelle optique avec des distorsions bien caractérisées, mais la fabrication synthétique de gyroïdes avec des dimensions unitaires supérieures à 200 nm reste très difficile à réaliser.
La nature offre une alternative. Plusieurs espèces de papillons, dont Callophrys rubi, Parides sesostris et Teinopalpus imperialis, produisent des cristaux photoniques gyroïdes dans leurs écailles alaires par auto-assemblage biologique contrôlés. Ces réseaux monogyroïdes possèdent des cellules unitaires d'environ 300 nm organisées en domaines polycristallins, avec des textures de domaines reproductibles et des populations de défauts bien définies. Ils constituent des systèmes modèles pour l'étude des défauts topologiques dans les réseaux photoniques 3D aux longueurs d'onde visibles.
L'objectif de cette thèse est d'observer, classifier et caractériser quantitativement les défauts topologiques dans ces cristaux photoniques biologiques en trois dimensions, et de déterminer si les distorsions de réseau aux joints de domaines produisent des états photoniques topologiques. La thèse suit une approche multi-échelle. D'abord, nous caractérisons les architectures de domaines de plusieurs espèces par microscopie électronique et optique. Ensuite, nous imagerons des écailles entières encore attachées aux fragments d'aile par tomographie X holographique et ptychographie en champ proche à une résolution de ~60 nm. Enfin, guidés par ces données, nous extrairons des écailles sélectionnées pour la laminographie ptychographique X à haute résolution (~20 nm) afin de mesurer le champ de distorsion 3D aux coeurs des défauts. Les volumes structuraux mesurés serviront d'entrées pour des simulations de structures de bandes photoniques testant si les distorsions produisent des points de Weyl. Le/la doctorant(e) développera la chaîne de traitement complète, de la segmentation des domaines à l'extraction des déformations, en s'appuyant sur nos travaux récents sur les réseaux diamantaires synthétiques (Karpov et al., Nature Nanotechnology, 2024).

Three-dimensional self-assembled networks, whether derived from block copolymers or formed biologically, are polycrystalline: they consist of oriented grains separated by boundaries where the lattice is distorted. Lu et al. [1] demonstrated that double-gyroid photonic crystals host Weyl points (Fig. 2) when parity symmetry is broken by structural perturbations. Weyl points are topological degeneracies in the photonic band structure that support protected surface states (Fermi arcs) at domain interfaces, with path-dependent propagation attractive for directional light guiding and angular filtering. Park et al. [2] and Jo et al. [3] then showed that non-affine lattice distortions arising during gyroid self-assembly from block copolymers break precisely this parity symmetry: directional contraction during desolvation produces triclinic structures with forbidden crystallographic reflections, providing direct evidence of inversion symmetry breaking. Grain boundaries, long considered detrimental to photonic crystal performance, may instead be the structural origin of topological physics at optical frequencies.
Several butterfly species produce single-gyroid chitin-based photonic crystals within their wing scales [8], including Callophrys rubi (Fig. 3), Parides sesostris, and Teinopalpus imperialis. In C. rubi, the network (space group I432, unit cell ~300 nm) is organized into polycrystalline domains of 2-10 µm [4,5]. The ~300 nm periodicity places potential Weyl degeneracies in the visible spectrum, and the near-equilibrium biological assembly produces reproducible domain textures with well-defined defect populations. Singer et al. [4] identified domain boundaries in T. imperialis by 2D X-ray scattering but could not map volumetric strain fields at specific interfaces. No existing technique has provided 3D distortion fields at real domain boundaries in an optically-scaled gyroid crystal.
In our recent work [6], we resolved ~70,000 unit cells in a synthetic gold diamond network (60 nm unit cell) at 11.2 nm resolution and identified topological defects with half-integer charges through the 3D Moiré strain analysis we developed for this purpose (Fig. 4). The method maps inter-domain distortion fields from interference fringes between mismatched domains and applies to any 3D periodic network. Extending this approach to the biological gyroids requires a multi-scale imaging strategy: pre-characterization with electron and optical microscopy to identify candidate defect architectures, holographic X-ray tomography and near-field ptychography (Fig. 3) at ~60 nm resolution to map domain landscapes on intact wing fragments, and ptychographic X-ray laminography [7] at ~20 nm resolution on extracted scales to measure the distortion fields at selected defect cores.

1. Develop a multi-scale pre-characterization framework combining electron microscopy, optical microscopy, and holographic X-ray tomography to identify and classify domain architectures and candidate defect sites across gyroid photonic crystals of multiple butterfly species (C. rubi, P. sesostris, T. imperialis).
2. Build statistical models of grain interactions that promote topological defect formation, using near-field ptychography at ~60 nm resolution on whole scales attached to wing fragments.
3. Acquire high-resolution (~20 nm) 3D maps of orientation and lattice distortion fields at selected defect sites by ptychographic X-ray laminography on extracted scales, and classify grain boundaries and topological defects using 3D Moiré strain analysis.
4. Determine whether the non-affine distortions measured at natural domain boundaries induce Weyl points in the photonic band structure, via FDTD and plane-wave expansion simulations.
5. Develop a multi-scale computational pipeline from domain segmentation to automated distortion field extraction, incorporating deep learning methods, applicable to other nanostructured periodic systems.

See Figure 1 for the Gannt chart.

Pre-characterization and species survey (Months 1-8). The candidate will survey domain architectures across three butterfly species (C. rubi, P. sesostris, T. imperialis) using SEM and optical microscopy on wing scales in situ, producing a catalogue of polycrystalline textures, boundary densities, and candidate defect sites. By month 6, one species will be selected based on domain quality, defect richness, and sample availability. Months 7-8 will complete the SEM catalogue for the selected species and plan sample logistics for the holographic campaign. In parallel, the candidate will familiarize themselves with reconstruction algorithms and computational tools.

Holographic X-ray tomography and near-field ptychography (Months 9-14). Wings from the selected species will be imaged at ~60 nm resolution at the ESRF (ID16A beamline) in a single beamtime campaign (see Fig. X). We have already established feasibility and optimized the framework from sample preparation to reconstruction in preliminary work (Fig. 3). This stage produces domain landscape maps and defect statistics to guide scale selection for laminography, and provides the candidate with hands-on training in synchrotron acquisition and phase retrieval before the more demanding laminography campaigns.

High-resolution ptychographic laminography (Months 15-20). Guided by the 60 nm data, the candidate will evaluate several mounting approaches (SiN membranes, carbon grids, free-standing) and assess the effects of gold sputtering on contrast and stability under X-rays at the ESRF ID16B beamline. Once the preparation protocol is established, PyXL measurements at the SLS (cSAXS beamline) will provide high-resolution 3D volumes of pre-identified regions. Laminographic reconstruction and distortion field extraction are more involved than for standard tomography, and the associated data analysis will extend into the computational analysis stage.

Multi-scale computational analysis (Months 12-25). In parallel with experiments, the candidate will develop the computational pipeline: (i) automated domain segmentation using deep learning trained on SEM and 60 nm X-ray data; (ii) 3D orientation field mapping by local Fourier analysis; (iii) distortion field extraction at grain boundaries by 3D Moiré strain analysis, building on [6]; (iv) topological defect classification and charge assignment. The pipeline develops first on the 60 nm data and then transfers to laminography volumes.

Photonic simulations (Months 25-32). Measured 3D structural volumes serve as direct inputs for FDTD and plane-wave expansion simulations testing whether non-affine distortions at natural domain boundaries transform trivial degeneracies into isolated Weyl points, and whether domain interfaces support Fermi arcs.

Thesis writing (Months 33-36). Manuscript preparation and thesis writing, with publications targeted throughout the project.