Multiple Andreev reflections in a quantum dot coupled to superconducting leads: Effect of spin-orbit coupling

We study the out of equilibrium current through a multilevel quantum dot contacted to two superconducting leads and in the presence of Rashba and Dresselhaus spin-orbit couplings, in the regime of strong dot-lead coupling. The multiple Andreev reflection (MAR) subgap peaks in the current-voltage characteristics are found to be modified (but not suppressed) by the spin-orbit interaction in a way that it strongly depends on the shape of the dot confining potential. In a perfectly isotropic dot the MAR peaks are enhanced when the strength αR and αD of Rashba and Dresselhaus terms are equal. When the anisotropy of the dot confining potential increases, the dependence of the subgap structure on the spin-orbit angle $theta=arctan(alpha_D/αlpha_R)$ decreases. Furthermore, when an in-plane magnetic field is applied to a strongly anisotropic dot, the peaks of the nonlinear conductance oscillate as a function of the magnetic-field angle and the location of the maxima and minima allows for a straightforward read-out of the spin-orbit angle $theta