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。

Characteristic Lengths in Superconductors

超导体中的特征长度

Arising in the theoretical and experimental investigations of superconductivity are two characteristic lengths, the London penetration depth and the coherence length.

在超导性的理论和实验研究中，出现了两个特征长度，即伦敦穿透深度和相干长度。

The London penetration depth refers to the exponentially decaying magnetic field at the interior surface of a superconductor. It is related to the density of superconducting electrons in the material. The fact of exclusion of magnetic fields from the interior of the superconductor is called the Meissner effect.

伦敦穿透深度指的是超导体内部表面处呈指数衰减的磁场。它与材料中超导电子的密度有关。将磁场从超导体内部排除的现象称为迈斯纳效应。

An independent characteristic length is called the coherence length. It is related to the Fermi velocity for the material and the energy gap associated with the condensation to the superconducting state. It has to do with the fact that the superconducting electron density cannot change quickly - there is a minimum length over which a given change can be made, lest it destroy the superconducting state. For example, a transition from the superconducting state to a normal state will have a transition layer of finite thickness which is related to the coherence length. Experimental studies of various superconductors have led to the following calculated values for these two types of characteristic lengths.

一个独立的特征长度称为相干长度。它与材料的费米速度以及与超导态凝结相关的能隙有关。这是因为超导电子密度不能迅速变化——存在一个最小的长度，在此长度范围内可以进行给定的变化，否则将破坏超导态。例如，从超导态过渡到正常态将有一个有限厚度的过渡层，该过渡层与相干长度有关。对各种超导体的实验研究得到了这两种特征长度的以下计算值。
Material
材料
Coherence length
ξ0(nm)
相干长度 ξ₀ (纳米)
London penetration depth
λL(nm)
伦敦穿透深度 λ_L (纳米)
Ratio
λL/ξ0
λ L /ξ 0 的比值
Sn
230
34
0.16
Al
1600
16
0.010
Pb
83
37
0.45
Cd
760
110
0.14
Nb
38
39
1.02
Data attributed to R. Meservey and B. B. Schwartz.
数据归R. Meservey和B. B. Schwartz所有。
 Index

Superconductivity concepts

Reference
Kittel,
Ch 12
索引 超导概念 参考 Kittel ，第12章
 
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London Penetration Depth in Superconductors

超导体中的伦敦穿透深度

One of the theoretical approches to the description of the superconducting state is the London equation. It relates the curl of the current density J to the magnetic field:

描述超导态的一种理论方法是伦敦方程。它将电流密度J的旋度与磁场相关联：

The London equation can be shown to require that the magnetic field exponentially decays to zero inside a superconductor (see Meissner effect discussion). The nature of the decay (see Chapter 12 of Kittel) depends upon the superconducting electron density n:

伦敦方程可以证明要求超导体内部的磁场指数衰减到零（见迈斯纳效应讨论）。衰减的性质（见Kittel第12章）取决于超导电子密度n：
Characteristic lengths in superconductors
超导体中的特征长度
 Index

Superconductivity concepts

Reference
Kittel,
Ch 12
索引 超导概念 参考 Kittel ，第12章
 
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Coherence Length in Superconductors

超导体的相干长度

One of the characteristic lengths for the description of superconductors is called the coherence length. It is related to the Fermi velocity for the material and the energy gap associated with the condensation to the superconducting state. It has to do with the fact that the superconducting electron density cannot change quickly - there is a minimum length over which a given change can be made, lest it destroy the superconducting state. For example, a transition from the superconducting state to a normal state will have a transition layer of finite thickness which is related to the coherence length.

描述超导体的一个特征长度称为相干长度。它与材料的费米速度和与超导态凝结相关的能隙有关。这是因为超导电子密度不能迅速变化——存在一个最小的长度，使得给定的变化可以在该长度范围内进行，否则会破坏超导态。例如，从超导态过渡到正常态将有一个有限厚度的过渡层，该过渡层与相干长度有关。
 Index

Superconductivity concepts

Reference
Kittel,
Ch 12
索引 超导概念 参考 Kittel ，第12章
 
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Meissner Effect from London Equation

从伦敦方程导出的迈斯纳效应

The London equation relates the curl of the current density J to the magnetic field:

伦敦方程将电流密度J的旋度与磁场相关联：

By relating the London equation to Maxwell's equations, it can be shown that the Meissner effect arises from the London equation. One of Maxwell's equations is

通过将伦敦方程与麦克斯韦方程联系起来，可以证明迈斯纳效应源于伦敦方程。麦克斯韦方程之一是

Using a vector calculus identity

使用矢量微积分恒等式

along with the curl of the Maxwell equation above

alongside the curl of the Maxwell equation above

and by substitution

并通过代换

Since


by Maxwell's equations, the value for B inside the superconductor must be identically zero unless the penetration depth is infinite (i.e., not a superconductor). This is one of the theoretical approaches to explaining the Meissner effect.

根据麦克斯韦方程，超导体内部的B值必须为零，除非穿透深度为无限大（即不是超导体）。这是解释迈斯纳效应的一种理论方法。
 Index

Superconductivity concepts

Reference
Kittel,
Ch 12
索引 超导概念 参考 Kittel ，第12章
 
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