Full counting statistics for transport through a molecular quantum dot magnet: Incoherent tunneling regime

Full counting statistics (FCS) of transport through a molecular quantum dot magnet is studied. Our analysis is theoretical, and its range of validity is restricted here to the incoherent tunneling regime. One of the original points is our Hamiltonian describing a single-level quantum dot, magnetically coupled to an additional local spin, the latter representing the total molecular spin s. We assume that the system is in the strong Coulomb blockade regime, i.e., double occupancy on the dot is forbidden. The master-equation approach to FCS is applied to derive a generating function yielding the FCS of charge and current. In the application of the master-equation approach to our system, Clebsch-Gordan coefficients appear in the transition probabilities, whereas the derivation of generating function reduces to solving the eigenvalue problem of a modified master equation with counting fields. The latter needs de facto only the eigenstate which collapses smoothly to the zero-eigenvalue stationary state in the limit of vanishing counting fields. Our main discovery is that in our problem with arbitrary spin s, some quartic relations among Clebsch-Gordan coefficients allow us to identify the desired eigenspace without solving the whole problem. Thus, the FCS generating function is derived analytically and exactly in the framework of the master-equation approach for an arbitrary value of spin s. By considering more specific cases, some contour plots of the joint charge-current probability distribution function are obtained numerically. The obtained FCS generating function is spin independent in the large bias regime, whereas for a small bias voltage, it suggests transport through our molecular quantum dot magnet looks exactly like that of a spinless fermion in the limit of large s. This rather counterintuitive consequence is subject to a direct experimental check.