Topology—a mathematical concept—has recently gained attention as an interdisciplinary topic encompassing condensed matter physics, solid-state chemistry, materials science, and electrical and mechanical engineering.1–3 The materials of interest include topological insulators, Dirac and Weyl semimetals, topological metals, and superconductors.4–6 It has been theoretically predicted that more than half of all materials are classified as topological.7 By analogy with the spin and electronic systems, topological concepts have been extended into phonons, resulting in the birth of topological phononics.8–10 It has been recognized that topological materials have connections with complex materials in biology where living organisms utilize mechanical, optical, and transport properties of biomolecular nanostructures. Topological chiral materials are another fascinating material class that exhibit topological order and chirality.11–15 Chirality refers to the property of an object that cannot be superimposed onto its mirror image. Among them are chiral nanomaterials replicating the biological topological order and mirror asymmetry. The absence of improper symmetries results in fascinating electronic properties, such as protected surface states across the Fermi surface.16–18 Chiral nanostructures from metals, semiconductors, and ceramics displayed giant optical activity19 and strong enantiomer-specific interactions with biological materials with comparable scale and topology.20 The twisted geometry of the chiral nanostructures gives rise to the emergence of chiral phonons—the propagating oscillatory motion originating from strongly correlated twist deformations of the crystal lattices.21–23 Topological and chiral matter offer potential for future applications in information processing. In particular, topological materials are regarded as candidates for addressing vulnerabilities caused by noise. This stimulates the search for topological superconductors and a deeper understanding of their physical properties. In this context, topological materials databases play a crucial role in accelerating the discovery of new materials with the desired properties.24–30 The field of topological and chiral matter has a connection to one-dimensional van der Waals materials since many of them reveal topological and chiral properties.31–37
The Special Topic issue on Topological and Chiral Matter—Physics and Applications highlights recent developments in theoretical, computational, and experimental physics of topological and chiral materials. This issue continues a series of Special Topic issues in Applied Physics Letters dedicated to strongly correlated materials and phenomena, featuring the research areas, in transition from complicated solid-state physics to applied physics. The prior issues dealt with charge-density wave materials,38 one-dimensional materials,39 phononics in low-dimensional materials,40 and fluctuations and noise phenomena.41 The current Special Topic issue features contributions that deepen the understanding of topological and chiral materials, guide the search for new materials, and address approaches for tuning such materials for future applications. The topics covered in the issue include topological semimetals, topological superconductors, topological electronic insulators, Dirac and Weyl semimetals, photonic topological insulators, and chiral nano and metamaterials. The issue also discusses optical topology, phononic topological and chiral materials, the theory of topological and chiral matter for material optimization and applications, and reconfigurable topological matter.
The unusual feature of this Special Topic issue is that there are more theoretical and computational contributions than experimental ones. This fact indicates that the experiments in the field are complicated and the field is still in its early stage of development. The theoretical and computational contributions of this issue describe silicon photonic topological insulators,42 Kagome materials with the quantum anomalous Hall effect,43 multi-topological states in one two-dimensional photonic crystals,44 electrically controllable chiral phonons in ferroelectric materials,45 selection of the frequency modes with Floquet exceptional points and chiral Zener tunneling,46 multi-band acoustic router by hybridizing distinct topological phases,47 chiral and directional optical emission from a dipole source,48 and topological light guiding and trapping via shifted photonic crystal interfaces.49 A distinct group of papers deal with magnetic and superconducting materials, featuring magnetic vortex control with current-induced axial magnetization in centrosymmetric Weyl materials,50 magnetic topological Kondo semimetal phases of matter,51 high-topological-number skyrmions with tunable diameters,52 magnetic topological textures such as interlayer antiferromagnetic frustrated bimerons and interlayer skyrmions with strain,53 and topological phase transitions with gapless topological superconductivity in magnet–superconductor hybrid platform.54 Several theoretical contributions address materials with functionalities such as giant magnetoresistance effect based on optically induced anti-chiral edge state in graphene,55 topological semimetal interface resistivity scaling,56 and topological invariants for encoding and manipulating chiral phonon devices.57
The experimental contributions of the issue highlight cubic Mn3Ge as a candidate material for topological antiferromagnetic spintronics,58 Bi2Se3 topological insulator nanowires and their potential for anisotropic optical and optoelectronic applications,59 spin–orbit torque generated by topological semimetal YPtBi,60 high spin Hall angle in BiSb topological insulators,61 topological and chiral superconductor nanoarchitectures,62 ultrafast spin dynamics of the prototypical topological insulator Bi2Se3,63 and phonon polaritons-induced photonic spin Hall effect in an α-MoO3 thin film.64 Several contributions discuss potential applications of topological and chiral matter. They describe the chiral structures with a spatial spiral arrangement of Fe3O4 nanoparticles for optimized energy dissipation,65 the engineering of the topological states of Weyl ferromagnetic CoxMnGay films grown by molecular beam epitaxy,66 and an experimental demonstration of topologically protected electroacoustic states.67
In conclusion, this Special Topic issue provides a glimpse of vibrant and innovative theoretical and experimental research in topological and chiral matter. We hope this Special Topic issue will be of interest to graduate students and researchers in academia.
The Editors want to thank all authors who contributed to this Special Topic issue of Applied Physics Letters. They are indebted to Dr. Subhajit Ghosh, UCLA, for his help with references and critical reading of the editorial. Special thanks go to Dr. Nikaela W. Bryan, Journal Manager, and Ms. Jessica Trudeau, Editorial Manager, for their help with this issue.