Interplay of spin orbit interaction and Andreev reflection in proximized quantum dots

Abstract

We investigate a hybrid device consisting of two quantum dots placed between a BCS superconductor and a semiconductor with a strong spin-orbit interaction. Assuming charge tunneling between quantum dots through spin-flip processes, we study the molecular Andreev bound states appearing in the proximized quantum dots. We show that the spin-orbit coupling splits a pair of the Andreev states into four in-gap quasiparticles. For the appropriate set of model parameters, two of these internal quasiparticle states merge, forming the zero-energy state. Under such circumstances, we obtain fully spin-polarized versions of the Majorana quasiparticles, localized on different quantum dots. This happens solely when the spin-orbit interaction is equally strong to the magnitude of crossed Andreev reflections, i.e. in the sweet spot. Otherwise, these processes are competitive, as can be observed in changes of the expectation values of the corresponding order parameters. We analyze signatures of such competition manifested under the nonequilibrium conditions for various configurations of the bias voltage. In particular, for the symmetric bias voltage between the normal electrodes and the Cooper pair splitter bias configuration, we reveal duality in the transport properties. Charge transport through the zero-energy state at the sweet spot is contributed by perfectly entangled electrons with an (almost) ideal transmission. Transport studies would thus enable empirical detection of the molecular quasiparticle states and the efficiency of dissipation processes caused by the external normal electrodes.