Reentrant localization of single-particle transport in disordered Andreev wires

We study effects of disorder on the low energy single-particle transport in a normal wire surrounded by a superconductor. In addition to the Andreev diffusion that decreases with increase in the mean free path $\ell$, the heat conductance is found to include the diffusive drift produced by a small particle-hole asymmetry, which increases with increasing $\ell$. The conductance thus has a minimum as a function of $\ell$ leading to a peculiar reentrant localization as a function of the mean free path.

Figure 1

Number of conducting modes (upper curve) normalized to that in a Sharvin contact, $\nu =N∕N_{\mathrm{Sh}}$, as a function of $\ell$ interpolated according to Eqs. (1, 2, 3, 4) for the wire length $d⪢a(v_F∕v_g)$. The gray area at the bottom is the localization region, $N\sim 1$ corresponding to ${\nu }_{\mathrm{loc}}\sim {\left(k_{F}a\right)}^{-2}$.

Figure 2

Trajectories for particles (1), (3) and holes (2), (4).