Persistent destructive quantum interference in the inverted graph method

Abstract

We formulate a general criterion that underlies the persistence of conductance zeros induced by destructive quantum interference under the application of external perturbations in physical systems described by a discrete nonsingular Hamiltonian $H$. Our approach uses nonzero matrix elements of ${H}^{\ensuremath{-}1}$ between two lattice points as edges of a graph to indicate the existence of a nonzero conductance between the same points. A given conductance zero, or a missing edge in the inverted graph, is preserved when the perturbation, in the form of on-site or additional interpoint hopping energies, is applied only to points outside the set of first-order graph neighbors of either the entry lead or the exit lead. We discuss the application of these results to a study of the robustness of the conductance zeros in the fulvene and benzene molecules.