A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilsons idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.

Negative differential conductance induced by electronic correlation in a double quantum-dot molecule

Electron tunneling through a two stage Kondo system constituted by a double quantum-dot molecule side coupled to a quantum wire, under the effect of a finite external potential is studied. We found that $I$-$V$ characteristic shows a negative differential conductance region induced by the electronic correlation. This phenomenon is a consequence of the properties of the two stage Kondo regime under the effect of an external applied potential that takes the system out of equilibrium. The problem is solved using the mean-field finite-$U$ slave-boson formalism.