Towards 4 formalisms description of properties of the unconventional Josephson junction and unconventional SQUIDs made by putting non-superconducting strip on the top of superconducting strip

TL;DR

This paper develops a theoretical framework using Ginzburg-Landau, Bogoliubov de Gennes, and Usadel formalisms to analyze unconventional Josephson junctions created by overlaying a non-superconducting strip on a superconducting strip, predicting a topological Meissner effect.

Contribution

It introduces a combined theoretical approach to study uJJs, solving non-linear equations numerically and predicting new physical phenomena like the topological Meissner effect.

Findings

Eigenenergies of uJJ obtained via combined GL and BdG methods

Prediction of the topological Meissner effect in uJJs

Numerical solutions of non-linear PDEs for simple cases

Abstract

We present the theoretical approach to study the unconventional Josephson junction (uJJ) made by putting the non-superconduncting strip on the top of superconducting strip. We work in the framework of the Ginzburg-Landau, Bogoliubov de Gennes and Usadel formalisms. We solve the non-linear parital differential equations numerically for few simple cases. We obtaine the eigenenergies of the uJJ by means of combined GL and BdGe method. cases. We predict the occurence of the physical effect, which we call the topological Meissner effect. Basing on the obtained results and current knowledge on Josephson junctions we point the future perspectives of the research on uJJs.