We present a dynamical mean-field theory (DMFT) study of the charge and orbital correlations in finite-size La$_{0.5}$Ca$_{0.5}$MnO$_3$ (LCMO) nanoclusters. Upon nanostructuring LCMO to clusters of 3 nm diameter, the size reduction induces an insulat
or-to-metal transition in the high-temperature paramagnetic phase. This is ascribed to the reduction in charge disproportionation between Mn sites with different nominal valence [Das et al., Phys. Rev. Lett. 107, 197202 (2011)]. Here we show that upon further reducing the system size to a few-atom nanoclusters, quantum confinement effects come into play. These lead to the opposite effect: the nanocluster turns insulating again and the charge disproportionation between Mn sites, as well as the orbital polarization, are enhanced. Electron doping by means of external gate voltage on few-atom nanoclusters is found to trigger a site- and orbital-selective Mott transition. Our results suggest that LCMO nanoclusters could be employed for the realization of technological devices, exploiting the proximity to the Mott transition and its control by size and gate voltage.
We have implemented the dynamical vertex approximation (D$Gamma$A) in its full parquet-based version to include spatial correlations on all length scales and in {sl all} scattering channels. The algorithm is applied to study the electronic self-energ
ies and the spectral properties of finite-size one-dimensional Hubbard models with periodic boundary conditions (nanoscopic Hubbard rings). From a methodological point of view, our calculations and their comparison to the results obtained within dynamical mean-field theory, plain parquet approximation, and the exact numerical solution, allow us to evaluate the performance of the D$Gamma$A algorithm in the most challenging situation of low dimensions. From a physical perspective, our results unveil how non-local correlations affect the spectral properties of nanoscopic systems of various sizes in different regimes of interaction strength.
