Figure 1

Abstract scheme of the nanosystems investigated: benzene geometry (top) and quantum point contact with 110 atoms (bottom). The individual nano-objects (blue sites) are connected by tunneling channels with amplitude $t$. These amplitudes might be rather complex and dependent on the distance as exemplified by the $t^{\prime }$ and $t^{\prime \prime }$ tunneling channels. The whole nano system is connected via some additional tunneling channels $V$ to the environment sketched schematically in red and orange and assumed to be noninteracting. Possible experimental realizations are coupled quantum dots or molecules connected to source and drain electrodes or a cluster of Fe atoms with the environment being a surface instead of the indicated geometry. Electronic correlations are particularly strong because of the nanostructuring.Reuse & Permissions

Figure 2

$\mathrm{Nano}\mathrm{\text{−}}\mathrm{D}\Gamma \mathrm{A}$ algorithm consisting of two self-consistency steps: (1) from the local Green function $G_{ii}$ and Coulomb interaction $U_i$ the $n$-particle fully irreducible vertex ${\Gamma }_{ii}^{\mathrm{irr}}$ has to be calculated; (2) from ${\Gamma }_{ii}^{\mathrm{irr}}$ a new Green function $G_{ii}$ is determined through the Dyson and parquet equation, respectively.Reuse & Permissions

Figure 3

On-site spectral function $\overline{A(0)}$ vs hybridization $V$, comparing $\mathrm{nano}\mathrm{\text{−}}\mathrm{D}\Gamma \mathrm{A}$ (lines) with the exact QMC solution (symbols) for two different geometries: hopping to two nearest neighbors only and hopping to all neighbors. Inset: Conductance between two opposite leads of the benzene ring, i.e., between the dark red leads of Fig. 1, for both topologies of neighborhood. Together with the low off-site-diagonal self-energy, the results show that $\mathrm{nano}\mathrm{\text{−}}\mathrm{D}\Gamma \mathrm{A}$ is reliable if either the hybridization strength is sufficiently strong or if the hopping is to sufficiently many neighbors.Reuse & Permissions

Figure 4

Conductance $G$ across the quantum point contact (QPC) of lower panel of Fig. 1 vs hybridization $t_{\mathrm{QCP}}$ between the two atoms of the QPC. $G$ becomes almost zero for $|t_{\mathrm{QCP}}|\lesssim 0.5t$. Inset: Spectral function layer by layer across the quantum point contact for two $t_{\mathrm{QCP}}$’s below and above the conductance increase, revealing a local Mott-Hubbard transition in the two atoms forming the QPC.Reuse & Permissions