Numerical Studies of Vortex Dynamics in Superconductivity

The behavior of vortex matter is critical to the applications of superconductivity and the effective control of Abrikosov vortices can lead to higher dissipation-free current carrying capacity (critical current). In this thesis, we study the superconducting vortex dynamics under different pinning potential systems via numerical simulations. We first show that on a moire pinning pattern, the critical current shows pronounced dips at commensurate angles due to vortices flowing in ordered quasi-one-dimensional channels. These flow channels break apart at incommensurate angles and for certain angles, the pinning pattern forms five-fold symmetry which can further suppress the easy flow channeling. We also study the vortex dynamics on the so-called 'Santa Fe ice' pining array and show that due to the frustrated geometry, the critical current profile of such a superconductor does not present any commensurability-induced peaks like the ones observed in other periodic patterns. When above the critical current, the vortices in Santa Fe pinning pattern develop both transverse and longitudinal flow channels while easy straight channels form in the square lattice. We also collaborate with an experiment group at Argonne National Lab and provide simulation evidence on the vortex flow in liquid state under different artificial spin ice configurations and show that the resistivity response in liquid state can be controlled by the underlying magnetic potential landscapes. We also present a thorough numerical study on the vortex ratchet motion induced by asymmetric potentials in such systems. At a more fundamental level, we propose a network science approach to systematically study the potential energy landscapes of confined vortex matter. We find that after mapping the full configuration space onto a complex network, the energetic property of the system is correlated with the topology of its network representation. In the vast majority of cases, the ground state of the system belongs to the sub-network with the highest number connections. Furthermore, with the large scale computing methods, we show that the system stability depends on the container symmetry, container size and vortex number.