London penetration depth: Difference between revisions
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{{short description|Distance to which a magnetic field penetrates into a superconductor}} |
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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 |
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^{-1}</math> times that of the magnetic field at the surface of the superconductor.<ref name=Kittel8thEd/> Typical values of |
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The London penetration depth results from considering the |
The London penetration depth results from considering the 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<ref name=Kittel8thEd/> |
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<math display="block">B(x) = B_0\exp\left(-\frac{x}{\lambda_L}\right),</math> |
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<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</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<ref name=Kittel8thEd/> |
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<math display="block">\lambda_L=\sqrt{\frac{m}{\mu_0 n q^2}},</math> |
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for [[charge carrier]]s of [[mass]] <math>m</math>, [[number density]] <math>n</math> and [[Electric charge|charge]] <math>q</math>. |
for [[charge carrier]]s of [[mass]] <math>m</math>, [[number density]] <math>n</math> and [[Electric charge|charge]] <math>q</math>. |
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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 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 K are very important to understand the mechanism of high-temperature superconductivity. |
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 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 K are very important to understand the mechanism of high-temperature superconductivity. |
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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 |
There are various experimental techniques to determine the London penetration depth, and in particular its temperature dependence. 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 |
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==References== |
==References== |
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{{reflist|refs= |
{{reflist|refs= |
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<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}} |
<ref name=Kittel8thEd>{{Cite book | last = Kittel | first = Charles | title = [[Introduction to Solid State Physics]] | publisher = John Wiley & Sons | year = 2004 | pages = [https://archive.org/details/isbn_9780471415268/page/273 273–278] | isbn = 978-0-471-41526-8 }} |
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</ref> |
</ref> |
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}}{{Superconductivity}} |
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}} |
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==See also== |
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*[[London equations]] 1935 |
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*[[Ginzburg-Landau theory]] 1950 |
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[[Category:Superconductivity]] |
[[Category:Superconductivity]] |
Latest revision as of 14:42, 3 May 2024
In superconductors, the London penetration depth (usually denoted as or ) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to times that of the magnetic field at the surface of the superconductor.[1] Typical values of
The London penetration depth results from considering the London equation and Ampère's circuital law.[1] If one considers a superconducting half-space, i.e. superconducting for x>0, and weak external magnetic field B0 applied along z direction in the empty space x<0, then inside the superconductor the magnetic field is given by[1]
The penetration depth is determined by the superfluid density, which is an important quantity that determines Tc in high-temperature superconductors. If some superconductors have some node in their energy gap, the penetration depth at 0 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 K are very important to understand the mechanism of high-temperature superconductivity.
There are various experimental techniques to determine the London penetration depth, and in particular its temperature dependence. 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
References[edit]
- ^ a b c d Kittel, Charles (2004). Introduction to Solid State Physics. John Wiley & Sons. pp. 273–278. ISBN 978-0-471-41526-8.
- ^ Fossheim, Kristian, and Asle Sudbø. Superconductivity: physics and applications. John Wiley & Sons, 2005.