Theoretical fundamentals of the emerging electronic phenomena in CUrved SupercONDuctor nanoArchitectures (CUSONDA)

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While all fundamental laws of nature are formulated locally, topology finds wide application in analysis of laws and patterns springing out of global structure of the system under consideration, providing new effects and phenomena. The objective of the present project is to elaborate conceptual fundamentals and to analyze topologic matter and its possible geometric design in curved superconductor micro- and nanostructures. It is motivated by the ongoing progress in fabrication of complex 3D nanoarchitectures (like open nanotubes and nanohelices with single or multiple chiralities) by using the advanced 3D roll-up self-organization and nanoprinting techniques based on focused ion beams. The emerging nanoarchitectures lead to occurrence of totally novel, counterintuitive properties of superconductors and thereby promise a significant improvement of the figures-of-merit as compared to the available devices. The vortex dynamics and phase slip phenomena as a main reason for dissipation are the keys for understanding the transport characteristics of superconductors. Our preliminary measurements and simulations indicate a very complex superconducting-to-normal resistive transition, which makes it an ambitious task, to unveil possible underlying mechanisms. To this end, it is necessary to perform a dedicated theoretical analysis and numerical simulations, because a direct experimental visualization of vortex dynamics or phase slips on the ns-timescale is not possible with the present technology. While the implications of curvature properties have been unveiled for the topology of the Ginzburg-Landau functional defined on a compact Riemannian manifold, the effects of curvature in confined spaces remain terra incognita. Therefore, in our proposal we apply for support regarding mutually potentiating theoretical analysis and numerical simulations of perspective for applications superconductor nanoarchitectures concerted with ongoing experiments.