London penetration depth

In superconductors, London penetration depth (usually denoted as or ) characterizes the typical distance to which a magnetic field penetrates into a superconductor.

Typical values of are between 50 and 500 nm. Deep inside a type I superconductor the magnetic field is zero (Meissner effect).

For example, if one considers a superconducting semi-space at , and weak external magnetic field applied along z-direction in the empty space , then inside the superconductor the magnetic field is given by

i.e. is the distance across which magnetic field becomes times weaker. The above expression follows from the solution of the London equation with proper boundary conditions.

The penetration depth is determined by the superfluid density which is an important quantity determines T_c in High-temperature Superconductors. If some superconductors have some node in their energy gap, the penetration depth at 0K 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 0K are very important to understand the mechanism of High-Temperature superconductivity. London penetration depth can be measured by muon spin spectroscopy when the supereconductor doesn't 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 λ²(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 origin of superconductor to us.

Further reading

• Charles Kittel, Introduction to Solid State Physics, 8-th edition, John Wiley & Sons, (2004), ISBN 978-0471415268, pages 262 (Meissner Effect) and 273 (London equations).
• http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000094000012127001000001&idtype=cvips&gifs=yes

See also

• London equations 1935
• Ginzburg-Landau theory 1950