Simulating the static magnetic response of thin film superconducting devices

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Abstract: Quantitative understanding of the spatial distribution of magnetic fields and screening currents in two-dimensional (2D) superconductors and superconducting devices composed of thin films is critical to interpreting the results of magnetic measurements of such systems. A convenient numerical method for solving the static 2D London equation, which describes the linear magnetic response of 2D superconductors, was introduced by Brandt and Clem [Phys. Rev. B 69, 184509 (2004), Phys. Rev. B 72, 024529 (2005)]. Here, we outline the model and present an efficient, open-source Python implementation of Brandt and Clem’s matrix inversion method, which solves for the magnetic field and current distributions in devices composed of thin inhomogenous superconducting films of arbitrary geometry in the presence of trapped flux, vortices, and inhomogeneous applied fields. As a demonstration, we apply the model to scanning superconducting quantum interference device (SQUID) microscopy. Beyond magnetic microscopy, this tool can be used to model screening effects and calculate self- and mutual-inductance in superconducting devices, and simulate the magnetic response of inhomogeneous 2D superconductors.

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