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The superconducting coherence length is a measure of the size of a Cooper pair (distance between the two electrons) and is of the order of cm. The electron near or at the Fermi surface moving through the lattice of a metal produces behind itself an attractive potential of range of the order of 3 × 10 − 6 {\displaystyle 3\times 10^{-6}} cm ...
Multimode helium–neon lasers have a typical coherence length on the order of centimeters, while the coherence length of longitudinally single-mode lasers can exceed 1 km. Semiconductor lasers can reach some 100 m, but small, inexpensive semiconductor lasers have shorter lengths, with one source [4] claiming 20 cm. Singlemode fiber lasers with linewidths of a few kHz can have coherence ...
There are two London equations when expressed in terms of measurable fields: =, =. Here is the (superconducting) current density, E and B are respectively the electric and magnetic fields within the superconductor, is the charge of an electron or proton, is electron mass, and is a phenomenological constant loosely associated with a number density of superconducting carriers.
In 1953, Brian Pippard, motivated by penetration experiments, proposed that this would modify the London equations via a new scale parameter called the coherence length. John Bardeen then argued in the 1955 paper, "Theory of the Meissner Effect in Superconductors", [2] that such a modification naturally occurs in a theory with an energy gap ...
The penetration depth is determined by the superfluid density, which is an important quantity that determines T c 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 ...
Furthermore, the superconducting length scales show similar anisotropy, in both penetration depth (λ ab ≈ 150 nm, λ c ≈ 800 nm) and coherence length, (ξ ab ≈ 2 nm, ξ c ≈ 0.4 nm). Although the coherence length in the a - b plane is 5 times greater than that along the c axis it is quite small compared to classic superconductors such ...
Ginzburg–Landau theory introduced the superconducting coherence length ξ in addition to London magnetic field penetration depth λ. According to Ginzburg–Landau theory, in a type-II superconductor / > /. Ginzburg and Landau showed that this leads to negative energy of the interface between superconducting and normal phases.
Based on Landau's previously established theory of second-order phase transitions, Ginzburg and Landau argued that the free energy density of a superconductor near the superconducting transition can be expressed in terms of a complex order parameter field () = | | (), where the quantity | | is a measure of the local density of superconducting electrons () analogous to a quantum mechanical wave ...