Heat Transport in Proximity Structures

We study heat and charge transport through a normal diffusive wire coupled with a superconducting wire over the region smaller than the coherence length. Because of partial Andreev reflection of quasiparticles from the interface, the subgap thermal flow is essentially suppressed and approaches zero along with energy, which is specific for diffusive structures. Whereas the electric conductance shows a conventional reentrance effect, the thermal conductance $\kappa$ rapidly decreases with temperature which qualitatively explains the results of recent experiments. In the Andreev interferometer geometry, $\kappa$ experiences full-scale oscillations with the order parameter phase difference.

Figure 1

Two models of the NS interface: sandwich geometry (a), and inset geometry (b).

Figure 2

(a) Upper view of the model of the NS interface in Fig. 1, with the ballistic trajectories of the electrons (solid lines) and holes (dashed lines); (b) the geometry of houselike Andreev interferometer with the magnetic flux $\Phi$.

Figure 3

Temperature dependencies of $\kappa /{\kappa }_{\mathrm{N}}$ (a) and $G/G_{\mathrm{N}}$ (b) obtained by numerical solution of Eq. (1), in comparison with the Andreev model (dashed curves), at $L_{\mathrm{N}}=10{\xi }_0$.

Figure 4

Phase dependencies of the thermal (a) and electric (b) conductances in the geometry of house interferometer in Fig. 2b, for different temperatures ($L_{\mathrm{N}}=10{\xi }_0)$.