A steady-state study of the nonequilibrium properties of realistic materials: Application of the mixed-configuration approximation

We present the mixed-configuration approximation (MCA) based on the auxiliary master equation approach impurity solver to study multiorbital correlated systems under equilibrium and nonequilibrium conditions within dynamical mean-field theory (DMFT). We benchmark the method for bulk and layered SrVO$_3$ in equilibrium and apply it to a prototypical nonequilibrium geometry in which a voltage bias is applied perpendicular to the layer via reservoirs held at different chemical potentials. For bulk SrVO$_3$, MCA reproduces the metallic state at moderate interaction strengths, but it overestimates the weight of the lower band relative to quantum Monte Carlo (QMC) and fork tensor product state (FTPS) solvers. With respect to QMC and FTPS, MCA yields an earlier metal-to-insulator transition as the electron-electron interaction is increased. In layered SrVO$_3$ at equilibrium, MCA partially captures the orbital polarization in favor of the in-plane $xy$ orbital, although not as strong as in the DMFT-converged results obtained with QMC. However, when performing a one-shot impurity calculation initialized with the DFMT-QMC results, MCA yields orbital occupations which show a stronger charge polarization in favor of orbital $xy$. This suggests that our approach can be used to study multiorbital impurity problems when the focus is to assess properties without performing the full DMFT self-consistent loop. Finally, under applied bias, we observe a pronounced redistribution of orbital occupations, demonstrating that the method captures bias-driven orbital charge transfer in realistic materials in nonequilibrium conditions.

💡 Research Summary

The authors introduce the Mixed‑Configuration Approximation (MCA), a computationally inexpensive scheme for multiorbital dynamical mean‑field theory (DMFT) that leverages the auxiliary master equation approach (AMEA) as a single‑orbital impurity solver. In MCA the orbital space is split into a target orbital and a set of “configuration” orbitals. For each possible occupation configuration of the latter, the inter‑orbital interaction terms are reduced to effective single‑particle shifts of the target orbital’s on‑site energy. The resulting single‑orbital impurity problem is solved with AMEA, yielding a Green’s function that is weighted by the joint probability of the configuration. These joint probabilities are obtained recursively from conditional probabilities, allowing the method to scale to an arbitrary number of orbitals without exponential growth in the impurity‑solver cost.

The methodology is benchmarked on bulk and layered SrVO₃, a prototypical t₂g‑derived correlated metal. In equilibrium, MCA reproduces a metallic state for moderate Hubbard U, but it overestimates the lower Hubbard‑band weight compared with quantum Monte‑Carlo (QMC) and fork‑tensor‑product‑state (FTPS) solvers, and it predicts the metal‑to‑insulator transition at a lower U, indicating a systematic bias toward stronger correlations. For the layered geometry, MCA captures the tendency of the in‑plane xy orbital to become more occupied (orbital polarization), though the effect is weaker than in fully converged DMFT‑QMC calculations. When a one‑shot MCA calculation is initialized with the DMFT‑QMC solution, the xy occupation increases markedly, demonstrating that MCA can be used as a fast post‑processing tool to explore orbital charge redistribution without a full self‑consistent DMFT loop.

The authors then apply MCA to a nonequilibrium steady‑state setup where a voltage bias is applied perpendicular to the SrVO₃ layers via reservoirs at different chemical potentials. Under bias, MCA predicts a pronounced redistribution of electrons from the yz/zx orbitals to the xy orbital, i.e., a bias‑driven orbital charge transfer. This behavior is consistent with the expectation that an electric field can selectively populate orbitals with larger in‑plane character, potentially enabling voltage‑controlled orbital switching.

Overall, MCA offers a substantial reduction in computational effort while retaining the ability to describe key qualitative features of multiorbital correlated materials, both in equilibrium and under bias. Quantitative discrepancies in spectral weight and transition points remain, suggesting that MCA is best suited for rapid exploratory studies or as a complement to high‑precision solvers when full DMFT self‑consistency is not essential. Future work may focus on systematic corrections to improve quantitative accuracy and on extending the approach to more complex heterostructures and larger orbital manifolds.