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arXiv:1805.01020 · Physical review. B./Physical review. B

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

Irakli Titvinidze, Max Erich Sorantin, Antonius Dorda, Wolfgang von der Linden, Enrico Arrigoni

Published Jul 27, 2018• 10 citations
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Abstract

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.

DOI
10.1103/physrevb.98.035146

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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 UUU, 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.
We present improvements of a recently introduced numerical method [E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)] to compute steady-state properties of strongly correlated electronic systems out of equilibrium. The method can be considered as a nonequilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the nonequilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the correlated impurity, Nb{N}_{b}Nb​ uncorrelated bath sites, and two Markovian environments (sink and reservoir). Algorithmic improvements in the impurity solver allow to treat efficiently larger values of Nb{N}_{b}Nb​ than previously in DMFT. This increases the accuracy of the results and is crucial for a correct description of the physical behavior of the system in the relevant parameter range including a semiquantitative description of the Kondo regime. To illustrate the approach, we consider a monoatomic layer of correlated orbitals, described by the single-band Hubbard model, attached to two metallic leads. The nonequilibrium situation is driven by a bias voltage applied to the leads. For this system, we investigate the spectral function and the steady-state current-voltage characteristics in the weakly as well as in the strongly interacting limit. In particular, we investigate the nonequilibrium behavior of quasiparticle excitations within the Mott gap of the correlated layer. We find for low-bias voltage Kondo-type behavior in the vicinity of the insulating phase. In particular, we observe a splitting of the Kondo resonance as a function of the bias voltage.
We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.
We develop a nonequilibrium multi-orbital extension of the two-particle self-consistent theory and apply it to the bilayer Hubbard model as a minimal platform to investigate correlation effects in the presence of interlayer interactions and tunneling. The method determines vertex corrections in the spin and charge channels self-consistently at the two-particle level, thereby avoiding the spurious finite-temperature phase transitions that limit dynamical mean-field theory in two dimensions. We derive the spectral self-energy and implement the framework directly on the real-frequency axis within the Keldysh nonequilibrium Green's function formalism, enabling the treatment of both equilibrium and non-equilibrium steady states without relying on numerical analytic continuation. As an application, we demonstrate that a pseudogap can emerge in the bilayer Hubbard model when spin, charge, or excitonic fluctuations become sufficiently strong. Instabilities in different channels are also evaluated in an unbiased manner across the parameter space. Remarkably, we find that the excitonic susceptibility grows with increasing interlayer bias, before it gets suppressed at large biases by the charge imbalance between the layers. This work establishes a versatile and computationally efficient framework for investigating correlated multi-orbital systems under nonequilibrium conditions.
We present a numerical method for the study of correlated quantum impurity problems out of equilibrium, which is particularly suited to address steady-state properties within dynamical mean field theory. The approach, recently introduced by Arrigoni et al. [Phys. Rev. Lett. 110, 086403 (2013)], is based upon a mapping of the original impurity problem onto an auxiliary open quantum system, consisting of the interacting impurity coupled to bath sites as well as to a Markovian environment. The dynamics of the auxiliary system is governed by a Lindblad master equation whose parameters are used to optimize the mapping. The accuracy of the results can be readily estimated and systematically improved by increasing the number of auxiliary bath sites, or by introducing a linear correction. Here, we focus on a detailed discussion of the proposed approach including technical remarks. To solve for the Green's functions of the auxiliary impurity problem, a non-Hermitian Lanczos diagonalization is applied. As a benchmark, results for the steady-state current-voltage characteristics of the single-impurity Anderson model are presented. Furthermore, the bias dependence of the single-particle spectral function and the splitting of the Kondo resonance are discussed. In its present form, the method is fast, efficient, and features a controlled accuracy.
We study a simple model of photovoltaic energy harvesting across a Mott-insulating gap consisting of a correlated layer connected to two metallic leads held at different chemical potentials. We address, in particular, the issue of impact ionization, whereby a particle photoexcited to the high-energy part of the upper Hubbard band uses its extra energy to produce a second particle-hole excitation. We find a drastic increase of the photocurrent upon entering the frequency regime where impact ionization is possible. At large values of the Mott gap, where impact ionization is energetically not allowed, we observe a suppression of the current and a piling up of charge in the high-energy part of the upper Hubbard band. Our study is based on a Floquet dynamical mean-field theory treatment of the steady state with the so-called auxiliary master equation approach as impurity solver. We verify that an additional approximation, taking the self-energy diagonal in the Floquet indices, is appropriate for the parameter range we are considering.
We extend the nonequilibrium dynamical mean field (DMFT) formalism to inhomogeneous systems by adapting the ``real-space'' DMFT method to Keldysh Green's functions. Solving the coupled impurity problems using strong-coupling perturbation theory, we apply the formalism to homogeneous and inhomogeneous layered systems with strong local interactions and up to 39 layers. We study the diffusion of doublons and holes created by photoexcitation in a Mott insulating system, the time-dependent build-up of the polarization and the current induced by a linear voltage bias across a multilayer structure, and the photoinduced current in a Mott insulator under bias.