THEORY OF THE SUPERCONDUCTING STATE .1. THE GROUND STATE AT THE ABSOLUTE ZERO OF TEMPERATURE
THEORY OF THE SUPERCONDUCTING STATE .1. THE GROUND STATE AT THE ABSOLUTE ZERO OF TEMPERATURE
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DOI：
10.1103/physrev.79.845
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发表时间：
1950-01-01
期刊：
影响因子：
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通讯作者：
FROHLICH, H
中科院分区：
文献类型：
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作者：
FROHLICH, H
在布洛赫的电子传导理论中，晶格振动对电子的散射与振动量子的吸收或发射有关。正如在场论中一样，这产生了一种自能，它可以通过微扰论的应用来计算。作为泡利原理的结果，最有趣的项具有动量（0）空间中电子之间相互作用的形式。两个电子之间的相互作用，其能量差与它们的能量相比很小，具有最有趣的角度依赖性。粗略地说，对于能量相等但k方向不同的情况，它是排斥的，而对于其它情况，它是吸引的。如果足够强，它在基态导致动量空间中的分布不同于正常（费米）分布。如果是这种情况，则存在激发态，其中一些（AZ）电子鉴于它们在动量空间中的相互作用而集中在k空间中的狭窄区域中。这些状态是稳定的，因为它需要能量来移除其中一个电子。它们的能量比基态高出一个与（AZ）~成正比的项。实现上述基态（等同于超导态）的条件要求电子和晶格振动之间的相互作用超过一定值。借助于高温电导率理论，这个条件可以用0 ℃时的电阻率p来表示。我们发现，p_n ′（1/n=原子体积; v=每个原子的自由电子数）必须超过一个仅取决于普适常数的值。如果假设v= 1，除了锂之外的所有单价金属都不满足所需条件，但大多数超导体都满足。在绝对零度下，正常态和超导态之间的能量差约为每电子ms~（s=声速），因此，它具有与绝对零度的分数对应的正确大小。还没有应用到更高的温度或外场的影响。
In Bloch's theory of electronic conductivity the scattering of electrons by lattice vibrations is connected with the absorption or emission of vibrational quanta. Asin field theories this gives rise to a self-energy which can be calculated by application of perturbation theory. The most interesting term as a result of the Pauli principle has the form of an interaction between electrons in momentum(0) space. The interaction between two electrons whose energy difference is small compared with their energy has a most interesting angular dependence. Roughly speaking, it is repulsive for equal energies but different directions of k, and attractive otherwiso. If strong enough it leads in the ground state to a distribution in momentum space which is different from the normal (Fermi) distribution. If this is the case then excited states exist in which some (AZ} electrons in view of their interaction in momentum space are concentrated in a narrow region in k-space. These states are stable in the sense that it requires energy to remove one of the electrons. Their energies are higher than the ground state by a term proportional to (AZ)~. The condition that the above-mentioned ground state (identified with the superconducting state) is realized requires that the interaction between electrons and lattice vibrations exceeds a certain value. With the help of the theory of high temperature conductivity, this condition can be expressed in terms of the resistivity p at O'C. It is found that pnv~'(1/n= atomic volume; v= number of free electrons per atom) must exceed a value depending on universal constants only. If v= 1 is assumed, all monovalent metals except lithium do not satisfy the required condition, but most superconductors do. The energy difference between the normal and the superconducting stateat absolute zero is about ms~(s= velocity of sound) per electron. It has thus the correct magnitude cor-responding to a temperature of a fraction of a degree absolute. No application to higher temperatures or to the influence of external fields has been made yet.