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):
where
is the magnetic flux quantum
,
is the critical current density 
, and 
characterizes the inductance of the superconducting electrodes
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
and is given by the following expression (in SI):where
is the magnetic flux quantumMagnetic 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...
,
is the critical current density , and characterizes the inductance of the superconducting electrodeswhere
is the thickness of the Josephson barrier (usually insulator), are the thicknesses of superconducting electrodes, and are their London penetration depthLondon 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.