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.