Peltier effect in normal-metal–superconductor microcontacts

We have calculated the heat current in the normal-metal–insulator–superconductor contacts with arbitrary transparency of the insulator barrier. In the tunneling limit (small transparencies), the heat flow out of the normal metal reaches its maximum at temperature T≃0.3Δ. At higher values of transparency, the interplay between single-particle tunneling and Andreev reflection determines optimum transparency which maximizes the density of heat flow out of the normal metal. In clean contacts, the optimum transparency is about 0.1 at T=0.3Δ and decreases with temperature roughly as (T/Δ${)}^{3/2}$. In disordered contacts, disorder enhances Andreev reflection and shifts the optimum point towards smaller transparencies. The optimal ratio of the barrier resistance to the resistance of the normal electrode is ${\mathit{R}}_{\mathit{N}}$/${\mathit{R}}_{\mathit{T}}$≃0.01 at T=0.3Δ and decreases with temperature similarly to clean contacts. For disordered contacts we also plot current-voltage characteristics for arbitrary values of the ratio ${\mathit{R}}_{\mathit{N}}$/${\mathit{R}}_{\mathit{T}}$.