Thermal Conductance of Andreev Interferometers

We calculate the thermal conductance $G^T$ of diffusive Andreev interferometers, which are hybrid loops with one superconducting arm and one normal-metal arm. The presence of the superconductor suppresses $G^T$; however, unlike a conventional superconductor, $G^T/G_N^T$ does not vanish as the temperature $T\to 0$, but saturates at a finite value that depends on the resistance of the normal-superconducting interfaces, and their distance from the path of the temperature gradient. The reduction of $G^T$ is determined primarily by the suppression of the density of states in the proximity-coupled normal metal along the path of the temperature gradient. $G^T$ is also a strongly nonlinear function of the thermal current, as found in recent experiments.

Figure 1

Schematic of Andreev interferometers with two different geometries: (a) house and (b) parallelogram.

Figure 2

$G^T$ of the house interferometer [(a) and (b)] and the parallelogram interferometer [(c) and (d)] as a function of the normalized temperature $T/T_c$. (a) and (c) for different $L/L^{\prime }$; (b) and (d) for different $r$. The insets in (a) and (c) show the oscillations of $G_T$ as a function of the phase $\varphi$.

Figure 3

Density of states $N(E,x)$ for the house interferometer along the path of the thermal current for $r=0$ and $L/L^{\prime }=10$. (a) $\varphi =0$; (b) $\varphi =\pi$.

Figure 4

Solid lines represent the strongly nonlinear $G^T$ as a function of the thermal current $I^T$ for the house interferometer. Dashed lines illustrate the $\sqrt{I^T}$ dependence of $G^T$ at intermediate values of the thermal current.