Electric and Heat Transport in One-Dimensional SNS Junctions with Energy-Dependent Transmission

We investigate the phase-independent dc components of the electric and heat currents through a one-dimensional superconductor-normal-metal-superconductor (SNS) junction subject to chemical-potential and temperature differences between two superconducting reservoirs. Using a scattering approach based on the Bogoliubov-de Gennes equations, we incorporate multiple Andreev reflections while retaining the energy dependence of transmission through the normal region. We compare energy-independent, quantum-dot-type, and quantum-point-contact transmission profiles. At low bias, both currents exhibit nonlinear features associated with the superconducting gap and multiple Andreev reflections. Their responses to a temperature difference depend remarkably on the transmission profile. At a small finite bias, the electric current depends weakly on the temperature difference for the energy-independent and quantum-dot-type profiles, whereas the quantum-point-contact profile produces a pronounced nonlinear response. The heat current depends nonlinearly on the temperature difference for all three profiles over the parameter range investigated. These results highlight the role of the transmission profile in nonlinear electric and heat transport through SNS junctions and provide a microscopic reference for related transport studies in mesoscopic fermionic superfluid junctions.