Effects of superconductor size, surface roughness, and thermomagnetic coupling on vortex nucleation, penetration, and subsequent dynamics

Abstract

Abstract

Abstract Vortex behaviors and field-response characteristics are critical in determining the functional limits, operational modes, and electromagnetic properties of superconducting applications, yet they are influenced by multiple factors, including sample size, surface roughness, and thermomagnetic coupling. Here, within the generalized time-dependent Ginzburg-Landau (GTDGL) framework, we aim to reveal how these factors govern vortex nucleation, penetration, and dynamics, and to elucidate the underlying physical mechanisms. The reliability and applicability of our numerical simulations were validated by excellent agreement with previous theoretical results derived from Ginzburg-Landau theory via linear stability analysis. Our investigation of sample-size effects reveals that the cross-scale transition in magnetization behavior from macroscopically continuous to mesoscopically discontinuous, along with a shift from single to multiple penetration fields, arises from the competition among multiple complex interactions in spatially confined systems, with the dominant mechanism varying with the field. We further obtained a size-dependent, exponentially decaying relation for multiple penetration fields without invoking the London approximation or single-vortex assumption. To model realistic rough surfaces, we employed a trigonometric series expansion, analogous to a Fourier series, to construct surfaces with Gaussian-distributed surface heights. Simulations based on this surface model demonstrated that surface roughness breaks geometric symmetry and significantly weakens the surface barrier, leading to fundamental changes in magnetization behaviors and vortex nucleation patterns. Furthermore, simulations of GTDGL equations coupled with the thermal diffusion equation indicate that the stepwise magnetic-field-ramping mode facilitates thermal equilibration of the vortex-motion-induced temperature rise through sufficient diffusion, whereas the continuous mode yields non-periodic temperature oscillations owing to insufficient relaxation. Such thermomagnetically driven discrepancies in local temperature distribution across varying ramping modes and ambient temperatures give rise to markedly distinct magnetization responses and vortex dynamics. These insights into how these key factors govern vortex behaviors advance fundamental understanding of superconductivity and inform the optimization of superconducting devices.