Superconducting Proximity Effect in Magnetic Molecules

We studied the transport through magnetic molecules (MM) coupled to superconducting (S), ferromagnetic (F) and normal (N) leads, with the aim of investigating the interplay between the magnetism and the superconducting proximity effect. The magnetic molecules were modeled using the Anderson model with an exchange coupling between the electron spins and the spin of the molecule. We worked in the infinite superconducting gap limit and treated the coupling between the molecule and the superconducting lead exactly, via an effective Hamiltonian. For the F/N-MM-S systems we used a real-time diagrammatic perturbation theory to calculate the electronic transport properties of the systems to first order in the tunnel coupling to the normal or ferromagnetic lead and then analysed the properties with respect to the parameters of these models. For these systems we found that the current maps out the excitation energies of the eigenstates of the effective Hamiltonian and that various parameters in these systems can lead to a negative differential conductance. In the N-MM-S case the current had no overall spin dependence, but when the normal lead is instead ferromagnetic there was a spin dependence and both the electronic and molecular spin expectation values could take on non-zero values. We also found that the polarisation of the ferromagnetic lead suppresses the superconducting proximity effect. Furthermore in the N-MM-S case the Fano factor indicated a transition from Poissonian transport of single electrons to Poissonian transport of electron pairs as the superconducting proximity effect goes out of resonance, however in the F-MM-S case this did not occur. For the S-MM-S systems we calculated the equilibrium Josephson current and found that in the infinite superconducting gap limit no 0 − π transition was possible. Advantages of this study compared to related ones are that we allow for arbitrarily large Coulomb interactions and we take into account coupling to the superconducting lead non-perturbatively. This is however at the expense of working in the superconducting gap limit. Recently it has been possible to couple single molecules to superconducting leads. This study therefore aims to be indicative of the transport properties that will be observed in future experiments involving single magnetic molecules coupled to leads.