Soft self-assembly of Weyl materials for light and sound

Abstract

Soft materials can self-assemble into highly structured phases which replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound. Here, we present a bottom-up approach based on self-assembly to engineer three-dimensional photonic and phononic crystals with topologically protected Weyl points. In addition to angular and frequency selectivity of their bulk optical response, Weyl materials are endowed with topological surface states, which allows for the existence of one-way channels even in the presence of time-reversal invariance. Using a combination of group-theoretical methods and numerical simulations, we identify the general symmetry constraints that a self-assembled structure has to satisfy in order to host Weyl points, and describe how to achieve such constraints using a symmetry-driven pipeline for self-assembled material design and discovery. We illustrate our general approach using block copolymer self-assembly as a model system.

published version, SI are available as ancillary files, code and data are available on Zenodo at https://doi.org/10.5281/zenodo.1182581, PNAS (2018)

References in corpus (12)

• Topological modes bound to dislocations in mechanical metamaterials
• Double-Weyl phonons in transition-metal monosilicides
• Nonlinear conduction via solitons in a topological mechanical insulator
• Intrinsically polar elastic metamaterials
• Current-Voltage Characteristics of Weyl Semimetal Semiconducting Devices, Veselago Lenses and Hyperbolic Dirac Phase
• Electromagnetic Scattering Laws in Weyl Systems
• A group theoretical route to deterministic Weyl points in chiral photonic lattices
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• The Schrödinger Formalism of Electromagnetism and Other Classical Waves --- How to Make Quantum-Wave Analogies Rigorous
• On the Role of Symmetries in the Theory of Photonic Crystals
• Weyl nodes as topological defects of the Wannier-Stark ladder: From surface to bulk Fermi arcs
• Optical interface states protected by synthetic Weyl points

Cited by in corpus (13)

• Topological active matter
• Topological Sound
• A brief review of topological photonics in one, two, and three dimensions
• Axial-field-induced chiral channels in an acoustic Weyl system
• Dualities and non-Abelian mechanics
• Liquid-crystal-based topological photonics
• Non-Abelian charged nodal links in dielectric photonic crystal
• Elastic Weyl points and surface arc states in 3D structures
• Weyl points and topological surface states in a three-dimensional elastic lattice
• Symmetry-driven Phononic Metamaterials
• Generating Weyl semimetals from alkali metals
• Tracing chirality from molecular organization to triply-periodic network assemblies: Threading biaxial twist through block copolymer gyroids
• Localized degenerate solutions to the massless Dirac and Weyl equations