Transfer Matrix Formalism for Two-Dimensional (2D) Superconducting Material

Abstract

This study introduces a fundamental transfer matrix formalism for superconductors. The transfer matrix is constructed by solving Maxwell’s equations under the TM (Transfer Magnetic) mode configuration and including boundary conditions at the interface of the superconductors. This matrix enables an investigation of the scattering properties of electromagnetic wave interacting with superconducting surfaces. Then, reflection coefficient (𝑅) and transmission coefficient (𝑇) are derived from elements of the transfer matrix. This formalism provides a basis for understanding the interaction of electromagnetic waves with the surface of superconductors for advanced studies such as coherent perfect absorption (CPA), spectral singularities, and PT symmetry. The results highlight the influence of the London penetration depth on the reflection coefficient (𝑅), the transmission coefficient (𝑇) and transfer matrix. Additionally, surface currents resulting from TM mode configuration and Meissner effect, are also expressed in terms of the London penetration depth. In this context, we establish a foundation for studying the potential applications of superconductors.

Keywords

• Transfer matrix
• Superconductors
• London penetration depth
• TM mode configuration

References

1. London F., 1964, Superfluids. No. 2. c. in Structure of Matter Series, Dover Publications, https://books.google.com.tr/books? id=fK4PAQAAMAAJ google scholar
2. Mostafazadeh A., 2009, Phys. Rev. A, 80, 032711 google scholar
3. Mostafazadeh A., Sarısaman M., 2015, Phys. Rev. A, 91, 043804 google scholar
4. Oktay G., Sarısaman M., Tas M., 2020, Scientific Reports, 10, 3127 google scholar
5. Saif A. G., 1992, Physica Status Solidi B Basic Research, 171, 199 google scholar
6. SarısamanM.,TaşM.,2018,Journal of the Optical Society of America B Optical Physics, 35, 2423 google scholar
7. SarısamanM.,TaşM.,2019a,JournalofAppliedPhysics,126,163102 google scholar
8. Sarısaman M., Taş M., 2019b, Annals of Physics, 401, 139 google scholar

9. Sarısaman M., Taşdemir S., Rostamzadeh S., 2024, Journal of Physics Condensed Matter, 36, 405603 google scholar
10. Schmidt V. V., 2013, The Physics of Superconductors: Introduction to Fundamentals and Applications. Springer Science & Business Media google scholar
11. Tinkham M., 1974, Reviews of Modern Physics, 46, 587 google scholar
12. Tinkham M., Lobb C., 1989, in , Vol. 42, Solid state physics. Elsevier, pp 91–134 google scholar