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

平行场中层状超导体Lawrence-Doniach模型的周期涡旋晶格

Periodic vortex lattices for the Lawrence-Doniach model of layered superconductors in a parallel field

我们考虑层状超导体的Lawrence-Doniach模型，在该模型中，平行超导平面的堆叠通过约瑟夫森效应耦合。我们假设超导体被放置在一个外部磁场定向平行于超导平面和研究周期性的晶格结构的限制作为约瑟夫森耦合参数r趋于零。这种限制导致了物理学文献中讨论的“透明态”，这在非常各向异性的高温超导体中观察到，在足够高的外加磁场和临界温度以下。我们使用Lyapunov-Schmidt约化来证明能量最小化唯一地决定了最佳涡旋晶格的几何形状：Bulaevskii和Clem提出的周期2（在层中）阵列。最后，我们讨论了明显的冲突与以前的结果有限宽度的样本，其中在小耦合制度的最小值采取的形式“涡平面”（介绍了Theodorakis和Kuplevakhsky）。

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…