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We present a numerical study of the emergence of Majorana and Andreev boundstates in a system composed by two quantum dots, in which one of then iscoupled to a conventional superconductor, SC1, and the other connects to atopological superconductor, SC2. By controlling the interdot coupling we candrive the system from a two single (uncoupled) quantum dots to a double(coupled) dot system configurations. We employ a recursive Green's functiontechnique that provides us with numerically exact results for the local densityof states of the system. We first show that in the uncoupled dot configuration(single dot behavior) the Majorana and the Andreev bound states appear in anindividual dot in two completely distinct regimes. Therefore, they cannotcoexist in the single quantum dot system. We then study the coexistence ofthese states in the coupled double-dot configuration. In this situation we showthat in the trivial phase of the SC2, the Andreev states are bound to anindividual quantum dot in the atomic regime (weak interdot coupling) orextended over the entire molecule in the molecular regime (strong interdotcoupling). More interesting features is actually seen in the topological phaseof the SC2. In this case, in the atomic limit, the Andreev states appear boundto one of the quantum dots while a Majorana zero mode appears in the other one.In the molecular regime, on the other hand, the Andreev bound states take overthe entire molecule while the Majorana state remains always bound to one of thequantum dots.

Andreev and Majorana bound states in single and double quantum dot structures