![](http://image.absoluteastronomy.com/images//topicimages/noimage.gif)
Josephson penetration depth
Encyclopedia
In superconductivity
, Josephson penetration depth characterizes the typical length on which an externally-applied magnetic field
penetrates into the long Josephson junction
. Josephson penetration depth is usually denoted as
and is given by the following expression (in SI):
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-2.gif)
where
is the magnetic flux quantum
,
is the critical current density
, and
characterizes the inductance of the superconducting electrodes
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-7.gif)
where
is the thickness of the Josephson barrier (usually insulator),
are the thicknesses of superconducting electrodes, and
are their London penetration depth
s.
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
, Josephson penetration depth characterizes the typical length on which an externally-applied magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
penetrates into the long Josephson junction
Long Josephson junction
In superconductivity, a long Josephson junction is a Josephson junction which has one or more dimensions longer than the Josephson penetration depth \lambda_J. This definition is not strict....
. Josephson penetration depth is usually denoted as
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-1.gif)
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-2.gif)
where
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-3.gif)
Magnetic flux quantum
The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. The phenomenon of flux quantization was discovered B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Nabauer, in 1961...
,
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-4.gif)
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-5.gif)
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-6.gif)
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-7.gif)
where
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-8.gif)
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-9.gif)
![](http://image.absoluteastronomy.com/images/formulas/6/6/2669554-10.gif)
London penetration depth
In superconductors, the London penetration depth characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to 1/e times that of the magnetic field at the surface of the superconductor...
s.