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

<span style="color: rgb(119, 119, 119); font-family: Montserrat, sans-serif;">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.</span>