Charge redistribution in correlated heterostuctures within nonequilibrium real-space dynamical mean-field theory

We address the steady-state behavior of a system consisting of several correlated monoatomic layers sandwiched between two metallic leads under the influence of a bias voltage. In particular, we investigate the interplay of the local Hubbard and the long-range Coulomb interaction on the charge redistribution at the interface, in the paramagnetic regime of the system. We provide a detailed study of the importance of the various system parameters, like Hubbard U, lead-correlated region coupling strength, and the applied voltage on the charge distribution in the correlated region and in the adjacent parts of the leads. In addition, we also present results for the steady-state current density and double occupancies. Our results indicate that, in a certain range of parameters, the charge on the two layers at the interface between the leads and the correlated region display opposite signs, producing a dipolelike layer at the interface. Our results are obtained within nonequilibrium (steady-state) real-space dynamical mean-field theory, with a self-consistent treatment of the long-range part of the Coulomb interaction by means of the Poisson equation. The latter is solved by the Newton-Raphson method and we find that this significantly reduces the computational cost compared to existing treatment. As the impurity solver for real-space dynamical mean-field theory, we use the auxiliary master equation approach, which addresses the impurity problem within a finite auxiliary system coupled to Markovian environments.