Memristors, memcapacitors, and meminductors, collectively called memelements,represent an innovative generation of circuit elements whose properties dependon the state and history of the system. The hysteretic behavior of one of theirconstituent variables, under the effect of an external time-dependentperturbation, is their distinctive fingerprint. In turn, this feature endowsthem with the ability to both store and process information on the samephysical location, a property that is expected to benefit many applicationsranging from unconventional computing to adaptive electronics to robotics, toname just a few. For all these types of applications, it is important to findappropriate memelements that combine a wide range of memory states (multi-statememory), long memory retention times, and protection against unavoidable noise.Although several physical systems belong to the general class of memelements,few of them combine all of these important physical features in a singlecomponent. Her we demonstrate theoretically a superconducting memory structurebased on solitonic long Josephson junctions (LJJs). We show that the Josephsoncritical current of the junction behaves hysteretically as an external magneticfield is properly swept. According to the hysteretic path displayed by thecritical current, a LJJ can be used as a multi-state memory, with acontrollable number of available states. In addition, since solitons are at thecore of its operation, this system provides an intrinsic topological protectionagainst external perturbations. Solitonic Josephson-based memelements may findapplications as memories, and in other emerging areas such as memcomputing,i.e., computing directly in/by the memory.
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