View source for London penetration depth

In [[superconductors]], the '''London penetration depth''' (usually denoted as <math>\lambda</math> or <math>\lambda_L</math>) characterizes the distance to which a [[magnetic field]] penetrates into a superconductor and becomes equal to '''<math>e</math>'''<sup>−1</sup> times that of the magnetic field at the surface of the superconductor.<ref name=Kittel8thEd/> Typical values of &lambda;<sub>L</sub> range from 50 to 500&nbsp;nm.

The London penetration depth results from considering the [[London equations|London equation]] and [[Ampère's circuital law]].<ref name=Kittel8thEd/> If one considers a superconducting [[Half-space (geometry)|half-space]], i.e superconducting for x>0, and weak external magnetic field '''B'''<sub>0</sub> applied along ''z'' direction in the empty space x<0, then inside the superconductor the magnetic field is given by
:<math>B(x)=B_0\exp\left(-\frac{x}{\lambda_L}\right),</math><ref name=Kittel8thEd/>
<math>\lambda_L</math> can be seen as the distance across in which the magnetic field becomes [[e (math)|<math>e</math>]] times weaker. The form of <math>\lambda_L</math> is found by this method to be
:<math>\lambda_L=\sqrt{\frac{m}{\mu_0 n q^2}}</math>,<ref name=Kittel8thEd/>
for [[charge carrier]]s of [[mass]] <math>m</math>, [[number density]] <math>n</math> and [[Electric charge|charge]] <math>q</math>.

The penetration depth is determined by the [[superfluid]] density, which is an important quantity that determines ''T''<sub>c</sub> in high-temperature superconductors. If some superconductors have some node in their [[energy gap]], the penetration depth at 0&nbsp;K depends on magnetic field because superfluid density is changed by magnetic field and vice versa. So, accurate and precise measurements of the absolute value of penetration depth at 0&nbsp;K are very important to understand the mechanism of high-temperature superconductivity.

London penetration depth can be measured by [[muon spin spectroscopy]] when the superconductor does not have an intrinsic magnetic constitution. The penetration depth is directly converted from the depolarization rate of muon spin in relation which
''σ''(''T'') is proportional to ''λ''<sup>2</sup>(''T''). The shape of ''σ''(''T'') is different with the kind of superconducting energy gap in temperature, so that this immediately indicates the shape of energy gap and gives some clues about the origin of superconductivity to us.

==See also==
*[[Ginzburg–Landau theory]]
*[[BCS theory]]
*[[Superconducting coherence length]]

==References==
{{reflist|refs=
<ref name=Kittel8thEd>{{Cite book | last = Kittel | first = Charles | title = Introduction to Solid State Physics | publisher = John Wiley & Sons | year = 2004 | pages = 273–278 | isbn = 978-0-471-41526-8 | url-access = registration | url = https://archive.org/details/isbn_9780471415268 }}
</ref>
}}

[[Category:Superconductivity]]