Source and sink potentials for the description of open systems with a stationary current passing through

The authors present a model Hamiltonian for the description of open systems that exchange probability current density with their surroundings. The complex potentials appearing in this Hamiltonian act as source and sink, respectively, of probability current density. The primary applications of the theory of source and sink potentials are molecular electronic devices (MEDs), in the description of which the semi-infinite contacts are replaced by complex potentials. This is done in a rigorous manner, i.e., the exact wave function is recovered in the interior of the MED. To illustrate the approach, certain prototypical molecular conductors are considered in the Huckel approximation. The authors show that, for the examples considered, there exist almost isolated molecular states in the continuum of contact states that manifest themselves as Fano resonances in the transmission probability. The findings are confirmed by density functional theory calculations that also yield the predicted molecular states that are nearly decoupled from the contacts.