Figure 1

(a) Sketch of the molecular monolayer device. (b) Zoom in on two of the molecules in the upper panel, together with an energy-space representation of the molecular transmission resonances. Due to the intermolecular Coulomb interaction, the resonance seen by an electron tunneling into a molecule is shifted by $U$ if one of its neighbors is charged. (c) Level diagram showing tunneling into the LUMO of a single molecule. The LUMO is shifted by $kU$ when $k$ neighboring molecules are occupied (higher-lying dashed lines).Reuse & Permissions

Figure 2

(a) $I\left(V\right)$ and (b) $dI\left(V\right)/dV$ for a homogeneous monolayer with $\epsilon =10k_{B}T$ and increasing strength of the intermolecular Coulomb interaction $U=0,\cdots ,4k_{B}T$. We have assumed a square lattice configuration, where each molecule has $N=4$ nearest neighbors. $I$ and $dI/dV$ are given in arbitrary units (arb) since $I\propto \Gamma$ in the single-electron tunneling regime. The inset in (b) shows the linear conductance $G_T$ as a function of the position of the LUMO relative to the Fermi energy.Reuse & Permissions

Figure 3

(a) $\left|I\right|$ and (b) $dI/dV$ as a function of $V$ (thick lines) or $-V$ (thin lines) for $\epsilon =10k_{B}T$, $U=4k_{B}T$, and $N=4$. We vary the ratio between the source and drain tunnel couplings $\alpha ={\Gamma }_S/{\Gamma }_D$, while keeping $\overline{\Gamma }={\Gamma }_S{\Gamma }_D/({\Gamma }_S+{\Gamma }_D)$ fixed, which fixes the value of the current plateau at large $V$.Reuse & Permissions

Figure 4

$I\left(V\right)$ for $\epsilon =5U/2$, $N=4$, and successively lowered $T$. One molecule (out of nine) has ${\Gamma }_D={\Gamma }_S/100$. In the magenta curve we have furthermore assumed the LUMO of the asymmetrically coupled molecule to be $\delta \epsilon =U/4$ higher in energy compared with the others. The inset zooms in on the first current step.Reuse & Permissions

Figure 5

Current (upper panel) and differential conductance (lower panel) as a function of applied bias voltage. In each subfigure, results using the three different methods described above are shown: Mixed mean-field approximation (MMF), truncation of correlations (CORR), and exact diagonalization of a finite monolayer (ED). We have everywhere used $\epsilon =10k_{B}T$ and $N=4$ (square lattice). In ED we used a square lattice with $3\times 3$ molecules, all with the same properties, and periodic boundary conditions [using instead open boundary conditions (not shown) does not qualitatively alter the results, but merely leads to a small increase in the height of the first peak and reduced height of the satellite peaks, reflecting the fact that interactions are somewhat less important in this case]. The strength of the intermolecular Coulomb interaction is increased, with $U=k_{B}T$ in (a), $U=2k_{B}T$ in (b), $U=4k_{B}T$ in (c), and $U=6k_{B}T$ in (d).Reuse & Permissions