Calculation of the Magnetic Penetration Depth with the Mechanism of “Close-Shell Inversion” for Superconductors

Abstract

The mechanism of superconductivity is still controversial and there is no consensus on this topic, particularly on the high-temperature superconductivity. In an earlier work, we proposed a simple universal model of superconductivity called “close-shell inversion” [1]. Based on this model of superconductivity we proceed in the present work to calculate the superconducting magnetic penetration depth \(\lambda\) , a physical quantity that can be experimentally measured and verified with the theory. Due to the “close-shell inversion” effect, any unbalanced local magnetic field will cause a difference among the atomic magnetic moments of any two nearest-neighboring lattice atoms in the superconductor, resulting in a net induced atomic magnetic field against the externally applied magnetic field, which is thus gradually attenuated after some number of layers of lattice atoms. The superconducting magnetic penetration depth is just determined by counting the number of the layers because, at the last one of these layers, the magnetic field intensity is reduced to 1/e (with e; theEuler’s number) compared to that on the surface of the superconductor. The calculation results show that the net magnetic field decays exponentially from the surface to the interior of the superconductor, in agreement with the existing theories and experimental data, and are also compared with experimental measurement data, which are consistent. The equation of the penetration depth is also derived, which depends critically on the effective circulation radius of the conduction electron.