Controlling the Sign of Magnetoconductance in Andreev Quantum Dots

We construct a theory of coherent transport through a ballistic quantum dot coupled to a superconductor. We show that the leading-order quantum correction to the two-terminal conductance of these Andreev quantum dots may change sign depending on (i) the number of channels carried by the normal leads or (ii) the magnetic flux threading the dot. In contrast, spin-orbit interaction may affect the magnitude of the correction, but not always its sign. Experimental signatures of the effect include a nonmonotonic magnetoconductance curve and a transition from an insulator-like to a metal-like temperature dependence of the conductance. Our results are applicable to ballistic or disordered dots.

Figure 1

(a) A two-dimensional Andreev quantum dot in a three-terminal geometry, with two normal ($N$) and one superconducting ($S$) lead. (b), (c) The two possible two-terminal setups obtained from such a dot. Either (b) the $S$ lead is contacted to one of the $N$ leads, or (c) the $S$ lead is floating.

Figure 2

Contributions to $⟨T_{ij}^{ee}⟩$ (first three) and $⟨T_{ij}^{he}⟩$ (last four) considered in this Letter. Thick green (thin violet) paths indicate electrons (holes), dashed lines indicate complex-conjugated amplitudes. Normal leads are labeled $i$, $j$ while the $S$ lead is superconducting. The contributions are classified by the number of uncorrelated Andreev reflections ($ee0$ has none, $ee2\mathrm{I}$ and $ee2\mathrm{II}$ both have two). The full (open) squares on the $S$ lead indicate a factor of $\eta$ (${\eta }^{*}$) and the ellipses mark encounters.

Figure 3

Magnetoconductance curves for the setup of Fig. 1b. Left panel: $k_{B}T=0.1E_T$, and $N_R/N_L=n+0.2$, $n=0,1,2,\dots ,7$ (from bottom to top). Right panel: $N_R/N_L=0.2$ (dashed red line) and 7.2 (dot-dashed blue line), for $k_{B}T/E_T=0.1$, 1, 2, 4 and 8 (dashed: from bottom to top; dot-dashed: from top to bottom). For both panels, the vertical axis gives $\delta g_{\mathrm{qm}}$ in units of the conductance quantum $2e^2/h$ with channel numbers chosen such that $N_S^2{N}_L^2/(N_L+N_R{)}^3=5$ in all instances. Note the crossover from monotonic to nonmonotonic behavior of the magnetoconductance as $T$ increases, for $N_R/N_L=0.2$ (dashed curves).