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

虽然所有的基本自然法则都是局部制定的，但拓扑学在分析所考虑的系统的全局结构中产生的规律和模式方面得到了广泛的应用，提供了新的影响和现象。本项目的目标是阐述概念基础，分析弯曲超导体微纳米结构中的拓扑物质及其可能的几何设计。它的动机是通过使用基于聚焦离子束的先进的3D卷起自组织和纳米打印技术来制备复杂的3D纳米结构(如开放的纳米管和具有单或多个手性的纳米螺旋)的持续进展。新兴的纳米结构导致了超导体全新的、与直觉相反的性质的出现，从而有望显著改善与现有器件相比的品质因数。涡旋动力学和相移现象是理解超导体输运特性的关键，它是引起耗散的主要原因。我们的初步测量和模拟表明了一个非常复杂的从超导到正常电阻的转变，这使得揭示可能的潜在机制成为一项雄心勃勃的任务。为此，有必要进行专门的理论分析和数值模拟，因为目前的技术不可能在毫微秒尺度上直接实验可视化涡旋动力学或相移。虽然曲率性质对定义在紧致黎曼流形上的Ginzburg-Landau泛函的拓扑的影响已经被揭示，但受限空间中曲率的影响仍然是未知的。因此，在我们的提案中，我们申请支持与正在进行的实验相一致的超导纳米结构应用前景的相互增强的理论分析和数值模拟。

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.