Related papers: Space-Time Hopfion Crystals
Structured light fields embody strong spatial variations of polarisation, phase and amplitude. Understanding, characterization and exploitation of such fields can be achieved through their topological properties. Three-dimensional (3D)…
Hopfions, three-dimensional topological solitons characterized by nontrivial Hopf indices, represent a fundamental class of field configurations that emerge across diverse areas of physics. Despite extensive studies of isolated hopfions, a…
Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions that realise integer topological numbers in their configuration via…
Topological solitons have been studied for decades in classical field theories, and have started recently to impact condensed matter physics. Among those solitons, magnetic skyrmions are two-dimensional particle-like objects with a…
Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search of hopfions in real physical systems is going on for nearly half a…
Hopfions, as three-dimensional topologically nontrivial structures described by poloidal and toroidal winding numbers, hold promise as robust information carriers in spintronics, functional materials, and optical communications. Although…
Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime…
3D topological solitons are marvels of mathematical physics that arise in theoretical models in elementary particle and nuclear physics, condensed matter, and cosmology. A particularly interesting type of them is described by the…
Topological spin configurations, such as soliton-like spin texture and Dirac electron assemblies, have emerged in recent years in both fundamental science and technological applications. Achieving stable topological spin textures at…
We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
Topological spin textures exhibit a hierarchical nature. For instance, magnetic skyrmions, which possess a particle-like nature, can aggregate to form superstructures such as skyrmion strings and skyrmion lattices. Magnetic hopfions are…
Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…
Magnetic skyrmions are chiral spin textures which have attracted intense research for their fundamentally novel physics and potential applications as spintronic information carriers. The stability which makes them so potentially useful is a…
The recent research of topological photonics has not only proposed and realized novel topological phenomena such as one-way broadband propagation and robust transport of light, but also designed and fabricated photonic devices with…
The introduction of topology unravels a new chapter of physics. Topological systems provide unique edge/interfacial quantum states which are expected to contribute to the development of novel spintronics and open the door to robust quantum…
Topological particle-like excitations such as skyrmions and hopfions offer rich opportunities for spintronic and photonic applications. While skyrmions have been extensively studied, the stabilization mechanisms and phase behavior of…
Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, are widely investigated in the diverse areas ranging from high energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics…
Topological photonics has recently emerged as a very general framework for the design of unidirectional edge waveguides immune to back-scattering and deformations, as well as other platforms that feature extreme nonreciprocal wave…
The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogs, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have…
The ability of structured light to mimic exotic topological skyrmion textures, encountered in high-energy physics, cosmology, magnetic materials, and superfluids has recently received considerable attention. Despite their promise as…