London penetration depth: Difference between revisions
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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</math>'''<sup>-1</sup> times that of the magnetic field at the surface of the superconductor.<ref name=Kittel8thEd/> Typical values of λ<sub>L</sub> range from 50 to 500 nm. |
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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 medium occupying{{clarify|date=October 2015}} ''x''<sub>0</sub>, and weak external magnetic field '''B'''<sub>0</sub |
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 medium occupying{{clarify|date=October 2015}} ''x''<sub>0</sub>, and weak external magnetic field '''B'''<sub>0</sub> applied along ''z'' direction in the empty space ''x''<sub>0</sub>, then inside the superconductor the magnetic field is given by |
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:<math>B(x)=B_0\exp\left(-\frac{x}{\lambda_L}\right),</math><ref name=Kittel8thEd/> |
:<math>B(x)=B_0\exp\left(-\frac{x}{\lambda_L}\right),</math><ref name=Kittel8thEd/> |
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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 |
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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 |
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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Revision as of 13:50, 7 October 2015
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 -1 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 medium occupying[clarification needed] x0, and weak external magnetic field B0 applied along z direction in the empty space x0, then inside the superconductor the magnetic field is given by
can be seen as the distance across in which the magnetic field becomes times weaker. The form of is found by this method to be
- ,[1]
for charge carriers of mass , number density and charge .
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.
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
See also
- London equations 1935
- Ginzburg-Landau theory 1950