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Normal-State Metallic Behavior in Contrast to Superconductivity: An Introduction
Published in David A. Cardwell, David C. Larbalestier, I. Braginski Aleksander, Handbook of Superconductivity, 2023
The second characteristic length associated with the superconducting state is the so-called ‘penetration depth,’ λ. This length describes the distance required for magnetic fields to decay in going from a region of normal material into the perfectly diamagnetic superconductor [8]. This length arose from the pioneering work by F. London and H. London on the electrodynamics of superconductors and is sometimes called the London penetration depth. For essentially pure superconductors, the London penetration depth is controlled by the density of superconducting electrons ns and is given by: λL=mc24πnse21/2
Acceleration
Published in Rob Appleby, Graeme Burt, James Clarke, Hywel Owen, The Science and Technology of Particle Accelerators, 2020
Rob Appleby, Graeme Burt, James Clarke, Hywel Owen
where ns is the number density of Cooper pairs and 퐣퐬 is the current density induced in the superconductor's surface by an electric field E. This is known as the 2nd London equation. Using the London and Maxwell's equations we can show that the field will penetrate a short distance into a superconductor, known as the London penetration depth, λL, where the magnetic field parallel to the surface will decay though the superconductor as Hz=Hoexp−xλL,
The non-local form of BCS theory
Published in J. R. Waldram, Superconductivity of Metals and Cuprates, 2017
The London penetration depth λL(T) is the distance by which a magnetic field penetrates a clean superconductor in the London limit, ξ0 ≫ λ. At T = 0 it is a Fermi surface parameter which depends on the density of conduction electrons and their effective mass. Its temperature dependence is associated with the backflow of excitations discussed in Section 9.4, which was worked out by Bardeen, Cooper and Schrieffer. However, few superconductors are in this limit. Elastic scattering increases the penetration depth. In the dirty limit, and also in the Pippard limit of extreme nonlocality, the penetration depth is conveniently expressed in terms of the Mattis-Bardeen conductivity ratio σ2/σn. In these limits the form of Λ(T) is somewhat different from that of ΛL(T) (Figure 10.4(a)).
In-plane magnetic penetration depth in FeSe1-xSx (x = 0, 0.04, 0.09) and FeTe1-xSex (x = 0.40) single crystals
Published in Phase Transitions, 2019
G. Purohit, A. Pattanaik, P. Nayak
The expression for magnetization by Kogan et al. [32] is given below:where M is the magnetization, is the quantum of magnetic flux = 2.07 × 10−7 Gcm2, λexp is the London penetration depth and Ba is the applied magnetic field. Temperature-dependent in-plane penetration depth [32] is given byFrom dirty limit, one finds [35]Here, Δ(T) is the temperature-dependent energy and Δ(0) is the energy gap at zero temperature. As FeSe1–xSx(x = 0, 0.04, 0.09) [37] and FeTe1–xSex(x = 0.40) [38], single crystals are two gap superconductors, and following the same technique as done in the previous study [39], Equation (4) is splitted into two equations for larger and smaller gaps assuming that these energy gaps do exist along c-axis and ab-plane directions.