The software package 3D-MLSI is developed, which allows us to calculate the current distribution and to extract inductances from multi-layered high-T c and low-T c superconducting circuits. Both kinetic and magnetic inductances as well as the three-dimensional distribution of the magnetic field are taken into account. We discuss the numerical approach used in 3D-MLSI and some new features such as visualization of sheet currents and analysis of circuits with holes. As an example, we present a simulation of a high-T c double-layer transformer.

Vortices in quantum condensates exist owing to a macroscopic phase coherence. Here we show, both experimentally and theoretically, that a quantum vortex with a well-defined core can exist in a rather thick normal metal, proximized with a superconductor. Using scanning tunneling spectroscopy we reveal a proximity vortex lattice at the surface of 50 nm—thick Cu-layer deposited on Nb. We demonstrate that these vortices have regular round cores in the centers of which the proximity minigap vanishes. The cores are found to be significantly larger than the Abrikosov vortex cores in Nb, which is related to the effective coherence length in the proximity region. We develop a theoretical approach that provides a fully self-consistent picture of the evolution of the vortex with the distance from Cu/Nb interface, the interface impedance, applied magnetic field, and temperature. Our work opens a way for the accurate tuning of the superconducting properties of quantum hybrids.

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The problem of developing an efficient numerical method for inductance extraction of superconducting microstrip transmission lines is considered. The new method which is based on an accurate boundary reduction of the differential equation problem is suggested and compared with known techniques. For this method, the computer program and results of computations are presented. The new algorithm and it's computer realization are faster, less memory consuming, more stable, more precise and can be implemented to transmission lines with arbitrary cross-sections.