层状超导体中的Biot-Savart关联
Biot-Savart correlations in layered superconductors
摘要：
本文讨论了在层间Josephson耦合可以忽略的极限下，无限层状Ⅱ型超导体的超导到正常相变。我们将每一层都建模为热激发煎饼涡旋的中性气体。我们假设在同一层和不同层中的涡旋之间的主要相互作用是由这些涡旋感生的屏蔽电流之间的电磁相互作用。通过精确求解首阶重整化群流得到的主要结果是，尽管该模型是一个三维系统，但它的相变仍是一个Kosterlitz-无相变。虽然过渡本身是由二维饼状涡的解约束驱动的，但低温相的RG分析和高温相的平均场论揭示了这两个相具有三维相关性。其实验结果是，所测量的面内超流刚度的跳跃（其是2d Kosterlitz无量纲理论中的通用量）将接收小的非通用校正（在Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+x}$中为1%的量级）。这一总体情况使文献中表达的一些主张有了更可靠的分析基础，也解决了一些相互矛盾的观点。
英文摘要：
We discuss the superconductor to normal phase transition in an infinite-layered type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally excited pancake vortices. We assume the dominant interaction between vortices in the same and in different layers is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group flow, is that the phase transition in this model is a Kosterlitz--Thouless transition despite being a three--dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence of this is that the jump in the measured in-plane superfluid stiffness, which is a universal quantity in 2d Kosterlitz-Thouless theory, will receive a small non--universal correction (of order 1% in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$). This overall picture places some claims expressed in the literature on a more secure analytical footing and also resolves some conflicting views.
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