Abstract: Non-charge-based logic devices are promising candidates for future logic circuits. Interest in studying and developing these devices has grown dramatically in the past decade as they possess key advantages over conventional CMOS technology. Due to their novel designs, a large number of micromagnetic simulations are required to fully characterize the behavior of these devices. The number and complexity of these simulations place large computational requirements on device development. We use state-of-the-art machine learning techniques to expedite identification of their behavior. Several intelligent sampling strategies are combined with machine learning multi-class classification models. These techniques are applied to a recently developed exchange-driven magnetic logic scheme that utilizes direct exchange coupling as the main driver.

Abstract: The nonreciprocal charge transport property which depends on the polarity of the applied current, such as the diode effect and the rectification effect, is of great importance for both theoretical research and engineering application. The nonreciprocal transport property in superconductors generally requires to break both the spatial inversion symmetry and the time-reversal symmetry, and therefore becomes one of the fundamental issues in superconductivity. Of particular interest, the superconducting diode effect, which exhibits one-way superconductivity, can potentially be applied to dissipationless diode devices, as a consequence has received extensive attention in recent years. In this Ph. D thesis, we simulate vortex dynamics with heat dissipation by numerically solving time-dependent Ginzburg-Landau equations and heat transfer equation. The nonreciprocal transport properties of the following three superconducting systems are studied. We study a superconducting film patterned with a conformal pinning array and find a giant rectification effect which is consistent with the experimental observation. In presence of the funneling effect due to the geometry of the conformal pinning array, Joule heating of the accumulating vortices creates hot spots and drives the sample to the normal state. Meanwhile, the density gradient of vortex does not match the gradient of pinning. The two mechanisms together lead to the giant rectification effect. We study the nonreciprocal charge transport property in a pinning-free superconducting nano-ring. We systematically calculate the response of the ratchet signal to various parameters in both D.C. and A.C. currents. By analyzing the vortex potential, we find that the nonreciprocal transport property is caused by the asymmetry potential barriers for vortex entry and exit. We study a superconductor/nanoscale-magnetic-dot hybrid structure. It takes advantage of the external current to control the nucleation of vortex-antivortex pairs, and can produce superconducting diode effect without applied magnetic fields. Our vortex dynamics simulation details the progress of the superconducting-normal phase transition due to motion of vortex pairs and heat dissipation. The nonreciprocal transport properties of the above three systems are all based on the broken symmetry of spatial inversion, which is caused by the anisotropic pinning array, the asymmetric geometry, and the nonuniform distribution of the magnetic field, respectively. The mechanisms we discuss in this thesis do not require special property of the materials and thus can be applied to any kinds of conventional superconductors. The present studies would provide solid theoretical basis for the future design and application of the dissipationless superconducting devices.

Abstract: Superconductivity is one of the most important discoveries of the last century. With many applications in physics, engineering, and technology, superconductors are crucial to our way of living. Several material and engineering issues however prevent their widespread usage in everyday life. Comprehensive studies are being directed at these materials and their properties to come up with new technologies that will address these challenges and enhance their superconductive capabilities. In this context, numerical modeling plays an important role in the search of new solutions to existing material and engineering issues. The time-dependent Ginzburg-Landau (TDGL) theory is a powerful predictive tool for modeling the macroscopic behavior of superconductors. However most of the numerical algorithms developed so far are incapable of describing many basic properties of real superconducting devices, and are too slow on current hardware for large-scale numerical simulations necessary for their accurate description. Therefore, the purpose of this thesis is to develop high-performing numerical solutions that can correctly describe material features to be used as modeling tools of laboratory experiments. Some important innovations introduced in this work include the numerical modeling of nonrectangular geometrical shapes with complex electrical and insulating components, the inclusion of dynamic heating of the material, and the description of different types of material inhomogeneities. These encompass the principal features necessary for a complete description of the superconductive physics in real material samples. In this thesis a numerical solution is developed for modeling superconducting thin films and used to study the superconductive properties of three experimental configurations: the dynamics of vortex matter in a Corbino disk, the motion of ultrafast vortices in an hourglass-shaped microbridge, and the photon detection process in a meander-patterned nanowire. Moreover, a numerical solution is developed for modeling three-dimensional superconductors which are studied here for the first time in the type-I superconducting regime. These numerical algorithms are optimized to exploit the computational horsepower of graphics processing units (GPUs) and multicore central-processing unit (CPU) clusters such that they can achieve high-performance and be used to model large-scale problems previously impossible on conventional machines. Several computational tools are also designed to assist with the modeling of superconducting devices. These include a numerical library of the TDGL equations, a novel mechanism for the generation of complex geometries, a closed-form solver to conduct numerical simulations, and a graphics user interface (GUI) to visualize the dynamic behavior of superconductors. The contributions in this thesis ultimately push the boundaries on what is possible in state-of-the-art numerical modeling of superconductivity.

Abstract: Using state-of-the-art simulation methods, we optimized the performance of nanoscale superconducting scanning probe tips for advanced spatial imaging of magnetic fields. The systematic studies of the tips’ static properties as a function of the tilted magnetic field, geometric parameters, and material parameters were carried out. The sensitivity of different superconducting quantum interference devices (SQUIDs) to the magnetic field emanating from the magnetic nanoparticle, where the location of a magnetic nanoparticle is considered below the primary loop's center, was examined as a function of the primary and secondary loop dimensions. The main objective of the research was to characterize and optimize the performance of a nano-sized SQUID-on-tip (SOT) device. Optimal SOT sensitivity was sought, for different loop sizes, arm linewidth, and lead dimensions. Moreover, we revealed that a constriction in the loop arms of the SOT can substantially improve the sensitivity of the device. Finally, the properties of the theta-SOT device were examined in the presence of in-plane and out-of-plane magnetic field components, enabling nanoscale imaging of 3D distributions of the magnetic field. Altogether, the obtained results deliver an engineering solution for the optimum performance of the SOT device in desired conditions.

Abstract: The EPS Antwerp Young Minds (AYM) invited Prof. Nir Navon (Yale University) to hold a colloquium for the physics department. For an audience of students and researchers, Prof. Navon presented recent advances in ultracold quantum matter and research from his own lab. His experimental work paves the way to make toy models used by theorists a reality. We sat down afterwards to discuss ultracold physics, box traps and setting up a lab from scratch.