Simple approach for the two-terminal conductance through interacting clusters

Abstract

We present a new method for the determination of the two-terminal differential conductance through an interacting cluster, where one maps the interacting cluster into a non-interacting cluster of $M$ independent sites (where $M$ is the number of cluster states with one particle more or less than the ground state of the cluster), with different onsite energy and connected to the leads with renormalized hoppings constants. The onsite energies are determined from the one-particle (one-hole) excitations of the interacting cluster and the hopping terms are given by the overlap between the interacting $N$ particle ground state and the one-particle (one-hole) excitations of the interacting cluster with $N$-1 ($N$+1) particles. The conductance is obtained from the solution of a system of $M$+2 coupled linear equations. We apply this method to the case of the conductance of spinless fermions through an AB$_2$ ring taking into account nearest neighbors interactions. We discuss the effects of interactions on the zero frequency dipped conductance peak characteristic of the non-interacting AB$_2$ ring as well as the consequences of a particle number jump that occurs as the gate potential is varied.