Transport in superconductors: Finite Element Method for Quasiclassical theory
Title: Transport in superconductors: Finite Element Method for Quasiclassical theory
SNIC Project: SNIC 2022/22-6
Project Type: SNIC Small Compute
Principal Investigator: Kevin Marc Seja <>
Affiliation: Chalmers tekniska högskola
Duration: 2022-01-07 – 2022-08-01
Classification: 10304


We have developed a code that can simulate equilibrium properties and transport in two-dimensional (2D) superconducting systems. It is based on a Finite Element Method that solves the quasiclassical equations of motion for such systems. In this very general framework, different phenomena such as equilibrium properties as well as transport in open systems can be studied. Our aim is to use this code to study, specifically, the so-called phase crystals that have been extensively researched within the group. For very low temperature, a d-wave superconductor can developed spontaneous currents that form loop-like patterns throughout the entire superconductor. Within the group, these phase crystals have been extensively studied earlier. We aim here to investigate two questions that have not yet been answered. Firstly, how does the presence of (scattering) impurities affect this phase. Secondly, how does the presence of these current loops affect transport, and how do the geometric patterns change under external current flow. Both of these questions could not be answered in the old code existing in the group, while the newly-developed FEM has the possibility to answers these questions. This is also relevant to find experimental fingerprints for this phase which would make an experimental observation possible.