First critical field in the pinned three dimensional Ginzburg-Landau model of superconductivity

2025/07/15 by Díaz-Vera, Matías, Román, Carlos · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2507.10915

Abstract

We study extreme type-II superconductors described by the three dimensional magnetic Ginzburg-Landau functional incorporating a pinning term a_ε(x), which we assume to be a bounded measurable function satisfying b≤ a_ε(x)≤ 1 for some constant b>0. A hallmark of such materials is the formation of vortex filaments, which emerge when the applied magnetic field exceeds the first critical field H_c1. In this work, we provide a lower bound for this critical field and provide a characterization of the Meissner solution, that is, the unique vortexless configuration that globally minimizes the energy below H_c1. Moreover, we show that the onset of vorticity is intrinsically linked to a weighted variant of the isoflux problem studied in [C. Román, On the First Critical Field in the Three Dimensional Ginzburg-Landau Model of Superconductivity, Comm. Math. Phys. 367 (2019), no.1, 317--349. arXiv:1802.09390] and [C. Román, É. Sandier and S. Serfaty, Bounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem, Proc. Lond. Math. Soc. (3) 126 (2023), no.3, 1015--1062. arXiv:2110.06858]. A crucial role is played by the ε-level tools developed in [C. Román, Three dimensional vortex approximation construction and ε-level estimates for the Ginzburg-Landau functional, Arch. Ration. Mech. Anal. 231 (2019), no.3, 1531--1614. arXiv:1712.07604], which we adapt to the weighted Ginzburg-Landau framework.

Citations

• First Critical Field in the pinned three-dimensional Ginzburg--Landau Model: A matching upper bound
• Vortex lines interaction in the three-dimensional magnetic Ginzburg--Landau model
• On the Meissner state for type-II inhomogeneous superconductors
• The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length
• L^r-Helmholtz-Weyl decomposition for three dimensional exterior domains
• Magnetic Ginzburg-Landau energy with a periodic rapidly oscillating and diluted pinning term
• Mean-field dynamics for Ginzburg-Landau vortices with pinning and forcing
• Ginzburg-Landau model with small pinning domains

Cited by

• First Critical Field in the pinned three-dimensional Ginzburg--Landau Model: A matching upper bound

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• First Critical Field in the pinned three-dimensional Ginzburg--Landau Model: A matching upper bound
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• Magnetic Ginzburg-Landau energy with a periodic rapidly oscillating and diluted pinning term