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Topological solitons commonly appear as energy-minimizing field configurations, but examples of stable, spatially localized objects with coexisting solitonic structures and singular defects are rare. Here we use a nonpolar chiral liquid crystal system to show how twist domain walls can co-self-assemble with vortices to form spatially localized topological objects with spontaneous folding. These soliton–vortex assemblies, which we call ‘möbiusons’, have a topology of the molecular alignment field resembling that of the Möbius strip’s surface and package localized field excitations into folded structures within a confinement-frustrated uniform far-field background. Upon supplying energy in the form of electric pulses, möbiusons with different overall symmetries of structure exhibit folding-dependent rotational and translational motions, as well as topological cargo-carrying abilities that can be controlled by tuning the amplitude and frequency of the applied fields. We demonstrate on-demand transformations between various möbiusons and show examples of encoding information by manipulating folds in such structures. A model based on the energetics of solitons and vortices provides insights into the origins of the folding instability, whereas minimization of the Landau–de Gennes free energy closely reproduces details of their internal structure. Our findings may provide a route towards topology-enabled light-steering designs.

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Arising in many branches of physics, Hopf solitons are three-dimensional particle-like field distortions with nontrivial topology described by the Hopf map. Despite their recent discovery in colloids and liquid crystals, the requirement of applied fields or confinement for stability impedes their utility in technological applications. Here we demonstrate stable Hopf solitons in a liquid crystal material without these requirements as a result of enhanced stability by tuning anisotropy of parameters that describe energetic costs of different gradient components in the molecular alignment field. Nevertheless, electric fields allow for inter-transformation of Hopf solitons between different geometric embodiments, as well as for their three-dimensional hopping-like dynamics in response to electric pulses. Numerical modelling reproduces both the equilibrium structure and topology-preserving out-of-equilibrium evolution of the soliton during switching and motions. Our findings may enable myriads of solitonic condensed matter phases and active matter systems, as well as their technological applications.