寻找高温超导性：从门捷列夫到塞伯格-威滕，再到马德隆
Searching for high temperature superconductivity: From Mendeleev to Seiberg-Witten via Madelung and beyond
摘要：
近年来，高温超导体的研究取得了令人瞩目的进展。LaH（10）和CSH（8）在兆巴压力下的最高温度分别为250 K和288 K。最高可能的温度是通过使用大量的化学元素来实现的。根据经验，其中许多是由马德隆特殊原子组成的。这里提供了解释这一观察结果的理论背景。到目前为止，经验的马德隆规则控制着门捷列夫的周期性定律。虽然大多数元素都遵守这条规则，但也有一些例外。因此，根据实验结果从理论上推导它及其例外是有意义的。作为一个副产品，这样的研究产生了一些似是而非的解释马德隆异常原子在高温超导体设计中的作用。到目前为止，服从马德隆规则的原子及其例外情况都是借助于相对论Hartree-Fock计算来研究的。在这项工作中，我们重新获得的规则和例外分析。新开发的方法有望在量子多体理论，特别是在高温超导理论的价值。最后，新的方法涉及一些使用塞伯格-威滕（S-W）理论，称为扩展的金兹伯格-朗道超导理论。利用S-W理论的结果，从拓扑跃迁的角度解释了马德隆规则原子和马德隆例外原子的区别。本文还讨论了单原子结果对各元素固体的推广
英文摘要：
Recently,a noticeable progress had been achieved in the area of high temperature superconductors. The maximum temperature of 250K for LaH(10) and 288K for CSH(8) were reported at the megabar pressures. The highest possible temperatures were achieved by employing hydrides of chemical elements. Empirically, many of these are made of Madelung-exceptional atoms. Here the theoretical background is provided explaining this observation. The, thus far empirical, Madelung rule is controlling Mendeleev's law of periodicity. Although the majority of elements do obey this rule, there are some exceptions. Thus, it is of interest to derive it and its exceptions theoretically in view of experimental findings. As a by product, such a study yields some plausible explanation of the role of Madelung-exceptional atoms in the design of hightemperature superconductors. Thus far the atoms obeying the Madelung rule and its exceptions were studied with help of the relativistic Hartree-Fock calculations. In this work we reobtain both the rule and the exceptions analytically. The newly developed methods are expected to be of value in quantum many-body theory and, in particular, in the theory of high temperature superconductivity. Ultimately, new methods involve some uses of the Seiberg-Witten (S-W) theory known as the extended Ginzburg-Landau theory of superconductivity. Using results of the S-W theory the difference between the Madelung-regular and Madelung-exceptional atoms is explained in terms of the topological transition. Extension of this, single atom, result to solids of respective elements is also discussed
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