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arXiv · 1810.05671

Meissner Effect from Landau Problem

Paola Arias·J. Gamboa·F. Méndez·David Valenzuela
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Abstract

The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous magnetic fields exhibits Meissner effect that is unstable unless two-body interactions are added and vortices emerge. Using the scaling freedom we can write the Schrödinger equation in terms of the scales ratio $κ={ E}/{ m }\propto 1- T/T_c $ where the last identification is realised simply by using the Gizburg-Landau theory. We find our equations are valid in the superconducting regime, and it is not possible for the Cooper pairs amplitude to reach to a constant, non-zero value, and therefore the theory is unstable. The supersymmetric quantum mechanics version, by completeness, is also considered.

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Paola Arias, J. Gamboa, F. Méndez, David Valenzuela. 2018-10-12. Meissner Effect from Landau Problem. https://doi.org/10.1142/s0217732318502413

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