Particle–hole transport in a TBCCO superconducting single-channel NSNSNSN nanowire

High-temperature superconductors open new avenues for developing nanoscale superconducting circuits with potential applications in quantum information processing. In this study, we focus on the characterization of single-channel ballistic electron wave propagation in composite NSNSNSN nanowires using the high \(T_c\) superconductor TBCCO (\(\text {Tl}_2\text {Ba}_2\text {Ca}_2\text {Cu}_3\text {O}_{10+\delta }\)). These nanowires are designed to preserve the coherence of a superconducting state while maintaining the simplicity of a quasi-one-dimensional system. Our analysis determines the geometric and thermal conditions to build such nanowires. By examining the scattering matrix, we identify conditions under which quasi-bound states significantly influence the transmission and reflection amplitudes, thereby affecting particle and hole propagation. Furthermore, we explore the nearly ergodic scattering behavior at resonant energies, where the scattering system exhibits nearly equal probability for the various scattering outcomes.