平行场中层状超导体Lawrence-Doniach模型的周期涡旋晶格

小耦合极限下Lawrence-Doniach能量的极小化：平行场中有限宽度样本

Minimizers of the Lawrence-Doniach energy in the small-coupling limit: finite width samples in a parallel field

本文研究了层状超导体的Lawrence-Doniach模型，即有限宽样品在平行于超导层的磁场作用下的情形。我们提供了一个严格的分析的能量最小的限制相邻超导层之间的耦合趋于零。我们确定了一个独特的全球最小的吉布斯自由能在这个政权（“涡平面”），并揭示了一个序列的一阶相变约瑟夫森涡通过边界成核。通过退化扰动理论的基础上的Lyapunov-Schmidt分解，减少了劳伦斯-Doniach系统的有限维变分问题的小耦合限制进行了研究。最后，得到了扰动展开的有效半径的下界（根据模型中出现的各种参数）。

斜磁场下Lawrence-Doniach泛函的极小值

Minimizers of the Lawrence-Doniach Functional with Oblique Magnetic Fields

我们研究了层状结构超导体的Lawrence-Doniach能量的极小化，假定Floquet-周期边界条件。具体地说，我们考虑了在超导平面上倾斜施加恒定磁场的影响，在假设$s=\eps^α$与$0<α<1$的条件下，将其作为层间距$s\to 0$和Ginzburg-Landau参数$κ=\eps^{-1}\to\infty$。通过导出极小元能量的精确匹配上下界，我们确定了下临界场和通量格的方向，使之在参数$\eps$中达到最优阶.对于首阶，诱导场用$\RR^3$中的凸极小化问题表征。我们观察到一个“磁通锁定过渡”，其中磁通线被钉扎到水平方向的小倾角的应用领域，这是不存在于各向异性的金兹伯格-朗道模型的极小化。我们获得的能量分布表明存在“阶梯涡”，这在物理学文献中已定性描述。

Analysis of Minimizers of the Lawrence-Doniach Energy for Superconductors in Applied Fields

We analyze minimizers of the Lawrence-Doniach energy for layered superconductors occupying a bounded generalized cylinder, $ Ω\times[0,L]$, in $\mathbb{R}^3$, where $Ω$ is a bounded simply connected Lipschitz domain in $\mathbb{R}^2$. For an applied magnetic field $\vec{H}_{ex}=h_{ex}\vec{e}_{3}$ that is perpendicular to the layers with $\left|\lnε\right|\ll h_{ex}\llε^{-2}$ as $ε\rightarrow 0$, where $ε$ is the reciprocal of the Ginzburg-Landau parameter, we prove an asymptotic formula for the minimum Lawrence-Doniach energy as $ε$ and the interlayer distance $s$ tend to zero. Under appropria…

Convergence of the Lawrence-Doniach Energy for Layered Superconductors with Magnetic Fields near $H_{c_1}$

We analyze minimizers of the Lawrence-Doniach energy for three-dimensional highly anisotropic superconductors with layered structure. For such a superconductor occupying a bounded generalized cylinder in $\mathbb{R}^3$ with equally spaced parallel layers, we assume an applied magnetic field that is perpendicular to the layers with intensity $h_{ex}\sim|\lnε|$ as $ε\rightarrow 0$, where $ε$ is the reciprocal of the Ginzburg-Landau parameter. We prove compactness results for various physical quantities of energy minimizers, and derive a Gamma-limit of the Lawrence-Doniach energy as $ε$ and the i…

First critical field of highly anisotropic three-dimensional superconductors via a vortex density model

We analyze a mean field model for $3$d anisotropic superconductors with a layered structure, in the presence of a strong magnetic field. The mean field model arises as the $Gamma$-limit of the Lawrence-Doniach energy in certain regimes. A reformulation of the problem based on convex duality allows us to characterize the first critical field $H_{c_1}$ of the layered superconductor, up to leading order. In previous work, Alama-Bronsard-Sandier \cite{ABS} have derived the asymptotic value of $H_{c_1}$ for configurations satisfying periodic boundary conditions; in that setting describing minimizer…