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Abstract |
Superconducting materials have sparked significant research activity in recent years, particularly in the development of electronic devices. These devices are currently used or are expected to soon be applied in various areas, such as highly precise and low-cost field detectors, ultra-sensitive single-photon detectors, superconducting diodes, memory and communication technologies, artificial neurons, and even quantum computing, where they could serve as platforms for qubits. Interest in such devices has been renewed by the discovery of superconductivity in atomically thin materials, enabling the design of smaller, lighter, and more affordable superconducting devices. Moreover, the discovery of multicomponent superconductors—materials described by more than one condensate—has opened the door to new, rich emergent phenomena with both fundamental and practical significance. Given that the behavior of superconducting vortices under applied magnetic or electric fields can either enhance or impair device performance, understanding vortex dynamics under different conditions is crucial for optimizing device functionality. In this thesis, we investigate the equilibrium and dynamic properties of conventional single-band $s$-wave superconductors, as well as multicomponent systems with $s$- and $d$-wave pairing, by numerically solving the time-dependent Ginzburg-Landau equations. In the first part, we explore mesoscopic superconductors, where the system's response to an applied magnetic field exhibits unique features due to the small volume-to-area ratio, challenging the conventional classification into type I and type II materials. We then examine the vortex-antivortex creation and annihilation process in a superconducting film carrying a transport current, demonstrating that in sufficiently thick films, a new dynamical state—termed the “closed vortex loop”—emerges, where vortex and antivortex lines form a single loop before annihilation. We also propose possible experimental signatures of this state. Finally, we present a superconducting diode design, where a central superconducting film is flanked by two superconducting wires carrying DC currents. By optimizing the magnetic field profile from these currents, we identify conditions for maximum diode efficiency and show that the device can function as a half-wave rectifier. In the second part, we develop a semi-analytical method to assess the stability of flux states in two-band superconducting rings. After validating this model with numerical simulations, we explore the possibility of soliton states. Lastly, we study vortex matter in twisted bilayers with $d$-wave superconducting pairing, revealing the emergence of two distinct skyrmionic states at different twist angles. We demonstrate how their magnetic field profiles could serve as key indicators for detecting topological states in such heterostructures. |
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