Magnetic steps on the threshold of the normal state

Assaad, Wafaa

doi:10.1063/5.0012725

Cited by 6 publications

(4 citation statements)

References 39 publications

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“…The GL energy functional introduced above was extensively studied for constant or regular magnetic fields in smooth domains (see, e.g., [CDR,CR2,CR3,CR4,FK1] for the 2D case and [AG,FK2,FKP,FMP,P] for the 3D one) and in domains with corners at the boundary [Cor,CG1,CG2,Gia,HK]. More recently, 2D GL models with piecewise-constant magnetic fields were also considered in [Ass1,Ass2,AK,.…”

Section: Ginzburg-landau Theorymentioning

confidence: 99%

Almost flat angles in surface superconductivity

Correggi

Giacomelli

2021

Nonlinearity

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Type-II superconductivity is known to persist close to the sample surface in presence of a strong magnetic field. As a consequence, the ground state energy in the Ginzburg–Landau theory is approximated by an effective one-dimensional model. As shown by Correggi and Giacomelli (2021 Calc. Var. Partial Differential Equations in press), the presence of corners on the surface affects the energy of the sample with a non-trivial contribution. In (Correggi and Giacomelli 2021 Calc. Var. Partial Differential Equations in press), the two-dimensional model problem providing the corner energy is implicitly identified and, although no explicit dependence of the energy on the corner opening angle is derived, a conjecture about its form is proposed. We study here such a conjecture and confirm it, at least to leading order, for corners with almost flat opening angle.

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Section: Ginzburg-landau Theorymentioning

confidence: 99%

Almost flat angles in surface superconductivity

Correggi

Giacomelli

2021

Nonlinearity

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“…Among others, such solutions can be any superstructures of Meissner islands, stripes and vortices. To obtain those types of solutions, one needs to invoke sophisticated approaches of numerically solving the GL equations, for recent advances, one can see the works [46][47][48][49][50] and references therein. In the present study we employ the standard powerful approach where one introduces a fictitious time relaxation that brings the system to a stationary state [51][52][53].…”

Section: Numerical Proceduresmentioning

confidence: 99%

Emerging complexity in the self-dual theory of superconductivity

Sarmento,

Córdoba-Camacho,

Shanenko

et al. 2024

J. Phys.: Condens. Matter

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To describe the way complexity emerges in seemingly simple systems of nature requires one to attend to two principal questions: how complex patterns appear spontaneously and why a single system can accommodate their inexhaustible variety. It is commonly assumed the pattern formation phenomenon is related to the competition of several types of interactions with disparate length scales. The existence of conﬁgurations of qualitatively distinct morphology is attributed to the system frustration induced by the multi-scale interactions. This work explores an alternative approach through a mechanism that leads to a wide range of intricate and topologically non-trivial patterns. The mechanism is described by the self-dual Ginzburg-Landau theory and, possibly, other Maxwell-Higgs models. It gives rise to unique spatial ﬂux proﬁles observed in superconductors between the two conventional superconductivity types, I and II.

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“…For not-uniform magnetic field there are, in general, less results available in the literature. We mention here [2,3,5] for piecewise constant magnetic fields in dimension d = 2 and [35,36] for smoothly varying magnetic fields both in dimension d = 2 and d = 3.…”

Section: A Semiclassical Problemmentioning

confidence: 99%

On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$

Giacomelli¹

2022

Preprint

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We consider the Neumann realization of the magnetic laplacian in R 3 + , in the case in which the magnetic field has a piecewise constant strength and a uniform direction. This operator is expected to be an effective model in studying the threshold to the normal state for a 3D superconductor exposed to a discontinuous magnetic field. We review some recent results above the infimum of the spectrum of the aforementioned operator.

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Magnetic steps on the threshold of the normal state

Cited by 6 publications

References 39 publications

Almost flat angles in surface superconductivity

Almost flat angles in surface superconductivity

Emerging complexity in the self-dual theory of superconductivity

On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$

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