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arXiv 1302.0896cond-mat.supr-con
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非均匀场中二维超导薄膜的下临界磁场理论

Theory of the lower critical magnetic field for a two-dimensional superconducting film in a non-uniform field

Thomas R. Lemberger, John Draskovic

摘要:

我们考虑了二维超导薄膜在非均匀磁场($\mathbf{B_a}$)作用下的涡旋现象。该膜具有“无限”半径$R_f$,厚度$t$约等于相干长度$ξ$。线圈近似为点偶极子。我们发现,第一个出现的涡轴承状态有一个漩涡和一个反涡。当在原点处施加的垂直场$B_0$超过外部临界场:$B_{c1}^0 = \frac{4\sqrt{2}Λ}{R}\frac{Φ_0}{4πΛ^2}ln\left(\fracΛξ\right)$时,该状态的吉布斯自由能低于无涡旋状态,其中$\frac{Φ_0}{4πΛ^2}ln\left(\fracΛξ\right) \equiv B_{c1}^{2D}$是2-D中的本征临界场,$Λ\equiv 2λ^2/t$是Pearl引入的2-D穿透深度,$λ$是体穿透深度。前因子$4\sqrt{2}Λ/R$在强筛选方案$Λ/R \ll 1$中计算。$R$是施加的垂直场$B_{a,z}(ρ)$改变符号的径向距离。在实验室中,涡流效应的开始通常发生在远高于$B_{c1}^0$的场,这表明涡流被涡流-反涡流解束缚势垒或被钉扎抑制。

英文摘要:

We consider the first appearance of vortices in a two-dimensional (2-D) superconducting film exposed to a non-uniform magnetic field, $\mathbf{B_a}$, produced by a nearby coil. The film has "infinite" radius, $R_f$, and thickness $t$ about equal to the coherence length, $ξ$. The coil is approximated as a point dipole. We find that the first vortex-bearing state to appear has both a vortex and an antivortex. The Gibbs free energy of this state is lower than the vortex-free state when the applied perpendicular field, $B_0$, at the origin exceeds the external critical field: $B_{c1}^0 = \frac{4\sqrt{2}Λ}{R}\frac{Φ_0}{4πΛ^2}ln\left(\fracΛξ\right)$, where $\frac{Φ_0}{4πΛ^2}ln\left(\fracΛξ\right) \equiv B_{c1}^{2D}$ is the intrinsic critical field in 2-D, $Λ\equiv 2λ^2/t$ the 2-D penetration depth introduced by Pearl, and $λ$ is the bulk penetration depth. The prefactor, $4\sqrt{2}Λ/R$, is calculated in the strong-screening regime, $Λ/R \ll 1$. $R$ is the radial distance at which the applied perpendicular field, $B_{a,z}(ρ)$, changes sign. In the lab, the onset of vortex effects generally occurs at a field much higher than $B_{c1}^0$, indicating that vortices are inhibited by the vortex-antivortex unbinding barrier, or by pinning.

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