Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Cooper Pairs

库珀对

The behavior of superconductors suggests that electron pairs are coupling over a range of hundreds of nanometers, three orders of magnitude larger than the lattice spacing. Called Cooper pairs, these coupled electrons can take the character of a boson and condense into the ground state.

超导体的行为表明,电子对的耦合范围达到数百纳米,比晶格间距大三个数量级。这些耦合的电子被称为库珀对,它们可以表现出玻色子的特性,并凝聚到基态。
This pair condensation is the basis for the BCS theory of superconductivity. The effective net attraction between the normally repulsive electrons produces a pair binding energy on the order of milli-electron volts, enough to keep them paired at extremely low temperatures.

Further discussion
进一步讨论
Model of the attractive mechanism
吸引力机制模型
这种配对是BCS超导理论的基础。通常相互排斥的电子之间的有效净吸引力产生了一个数量级为毫电子伏的配对结合能,足以在极低温下保持它们的配对状态。
Index

Superconductivity concepts

Reference Rohlf,Ch 15
索引 超导概念 参考 Rohlf,第15章
 
HyperPhysics***** Condensed Matter
HyperPhysics ***** 凝聚态物理
R Nave
Go Back
返回





Cooper Pairs

库珀对

The transition of a metal from the normal to the superconducting state has the nature of a condensation of the electrons into a state which leaves a band gap above them. This kind of condensation is seen with superfluid helium, but helium is made up of bosons -- multiple electrons can't collect into a single state because of the Pauli exclusion principle. Froehlich was first to suggest that the electrons act as pairs coupled by lattice vibrations in the material. This coupling is viewed as an exchange of phonons, phonons being the quanta of lattice vibration energy. Experimental corroboration of an interaction with the lattice was provided by the isotope effect on the superconducting transition temperature. The boson-like behavior of such electron pairs was further investigated by Cooper and they are called "Cooper pairs". The condensation of Cooper pairs is the foundation of the BCS theory of superconductivity.

金属从正常态过渡到超导态的过程,其本质是电子凝聚到一个状态,该状态在它们之上留下一个能带空隙。这种凝聚现象在超流氦中也有所体现,但氦由玻色子组成——多个电子不能凝聚到同一个状态,这是由于泡利不相容原理。弗洛赫利奇首先提出,电子在材料中以成对的形式通过晶格振动耦合。这种耦合被视作声子的交换,声子是晶格振动能量的量子。对与晶格相互作用的实验证据由超导转变温度的同位素效应提供。这种电子对的玻色子行为后来由库珀进一步研究,这些电子对被称为“库珀对”。库珀对的凝聚是BCS超导理论的基础。

Resistance diagram
电阻图
Phase diagram
相图
Index

Superconductivity concepts

Reference Rohlf,Ch 15
索引 超导概念 参考 Rohlf,第15章
 
HyperPhysics***** Condensed Matter
HyperPhysics ***** 凝聚态物理
R Nave
Go Back
返回





A passing electron attracts the lattice, causing a slight ripple toward its path.
一个经过的电子吸引晶格,导致向其路径产生轻微的波动。

A model of Cooper pair attraction

Cooper对吸引力模型
Another electron passing in the opposite direction is attracted to that displacement.
另一个电子在相反方向通过时会被吸引到那个位移
Further discussion of mechanism
机制的进一步讨论
Index

Superconductivity concepts

Reference Rohlf,Ch 15
索引 超导概念 参考 Rohlf,第15章
 
HyperPhysics***** Condensed Matter
HyperPhysics ***** 凝聚态物理
R Nave
Go Back
返回





Model of Pair Attraction

电子对吸引力模型



A visual model of the Cooper pair attraction has a passing electron which attracts the lattice, causing a slight ripple toward its path. Another electron passing in the opposite direction is attracted to that displacement. This constitutes a coupling between electrons which can be depicted in a Feynman diagram.
As strange as such an interaction seems, it is experimentally supported by the isotope effect and the evidence for a condensation to a boson-like state at the critical temperature for superconductivity.
尽管这种相互作用似乎很奇怪,但它得到了超导临界温度下凝聚到玻色子态的证据以及同位素效应的实验支持。

一个 Cooper 对吸引力的视觉模型中,一个电子经过时吸引晶格,导致其路径上产生轻微的波动。另一个方向相反的电子被该位移吸引。这构成了电子之间的耦合,可以在费曼图中表示。
Index

Superconductivity concepts

Reference Rohlf,Ch 15
索引 超导概念 参考 Rohlf,第15章
 
HyperPhysics***** Condensed Matter
HyperPhysics ***** 凝聚态物理
R Nave
Go Back
返回





Isotope Effect, Mercury

汞的同位素效应

If electrical conduction in mercury were purely electronic, there should be no dependence upon the nuclear masses. This dependence of the critical temperature for superconductivity upon isotopic mass was the first direct evidence for interaction between the electrons and the lattice. This supported the BCS theory of lattice coupling of electron pairs.

如果汞中的电导 purely 由电子贡献,那么其不应依赖于核质量。超导临界温度对同位素质量的依赖性是首次直接证据,证明了电子与晶格之间的相互作用。这支持了BCS理论中的电子对晶格耦合理论。

It is quite remarkable that an electrical phenomenon like the transition to zero resistivity should involve a purely mechanical property of the lattice. Since a change in the critical temperature involves a change in the energy environment associated with the superconducting transition, this suggests that part of the energy is being used to move the atoms of the lattice since the energy depends upon the mass of the lattice. This indicates that lattice vibrations are a part of the superconducting process. This was an important clue in the process of developing the BCS theory because it suggested lattice coupling, and in the quantum treatment suggested that phonons were involved.

令人惊讶的是,一个电现象,如零电阻的转变,竟然涉及晶格的纯粹机械性质。由于临界温度的变化涉及与超导转变相关的能量环境的变化,这表明部分能量被用来移动晶格中的原子,因为能量取决于晶格的质量。这表明晶格振动是超导过程的一部分。这在发展BCS理论的过程中是一个重要的线索,因为它暗示了晶格耦合,并在量子处理中暗示了声子的参与。
Index

Superconductivity concepts

Reference Rohlf,Ch 15
索引 超导概念 参考 Rohlf,第15章
 
HyperPhysics***** Condensed Matter
HyperPhysics ***** 凝聚态物理
R Nave
Go Back
返回