Figure 1

(a) Graphical representation of the system described by the Hamiltonian (1). $|{\varphi }_{\text{tip}}\rangle$ and $|{\varphi }_{\text{sub}}\rangle$ are eigenstates of the two electrodes. The logical input are encoded in the value of $\alpha$ and $\beta$. (b) Population of $|{\varphi }_{\text{sub}}\rangle$ for $E=-1$ eV, $e=0$ eV, $k=-1/2$ eV, and $\varepsilon ={10}^{-2}$ eV. When $\alpha =\beta =0$ an eigenstate of the system has the same energy as $|{\varphi }_{\text{tip}}\rangle$ and $|{\varphi }_{\text{sub}}\rangle$. This leads to a maximum oscillation frequency. This is not the case for the other values of the logical input and consequently the oscillation frequency is much lower. The QHC design plays with the level-repulsion effect for some molecular states to be at or off resonance with the initial and target state.Reuse & Permissions

Figure 2

(a) Simplified QHC molecule inserted between two electrodes. The two electrodes are supposed to interact only with the first state of the simplified molecule through the couplings $\mathcal{V}$. These couplings are $\mathcal{V}=-0.15$ eV. (b) The transmission coefficient of the system represented in (a) calculated with the ESQC technique for different values of the logical input (solid black line). The $T(E)$ follows the same variation as the normalized oscillation frequency for the system represented in Fig. 1a (dashed blue line). The chemical potentials of the electrode define the integration region of the $T(E)$ (grey shaded area) that gives the output current intensity.Reuse & Permissions

Figure 3

(a) Impact of $\alpha$ on the system’s eigenstates indicated by the dotted blue, dashed red, and solid black curves. When $\alpha =0$ the HOMO lies between the chemical potential of the two electrodes that defines the integration region (grey shaded area) leading to a strong current intensity. If $\alpha$ is strong enough to push the HOMO out of the integration region, the current intensity drop to almost zero. (b) Current intensity when $\alpha$ and $\beta$ vary from 0 to 1. The smaller $\mathcal{V}$, the steepest the transition goes from a 1 to a 0 output. Values of the different physical quantities relative to the output status for the four input configurations.Reuse & Permissions

Figure 4

(a) The STM experimental setup used in this article. The trinaphthylene is physisorbed on Au(111). Each logical input, denoted $\alpha$ and $\beta$, controls the position of a given surface Au atom. When $\alpha =0$ the corresponding Au atom is moved away from the molecule. On the contrary when $\alpha =1$, this atom is STM manipulated toward the end of a naphtyl branch. $\beta$ controls the second Au atom in the same way. The output of this molecular logic gate is measured in the tunneling current intensity going from the tip to the substrate through the end of the third naphtyl branch. (b) Constant current STM experimental image of the trinaphthylene physisorbed on Au(111) with three Au atoms in its surrounding (scale: 4 nm $\times$ 4 nm).Reuse & Permissions

Figure 5

Top: The three experimental images obtained approaching successively none, one, and two Au atoms near the end of the naphtyl branches. Middle: Molecular model of the Au-trinaphthylene surface system when optimizing its atomic scale surface structure for the experimental and calculated images to converge scan by scan. This optimization demonstrates the displacement of the H atoms when approaching a Au atom to the molecule. Bottom: The theoretical ESQC-STM images of the trinaphtylene interacting with none, one, and two surface atoms.Reuse & Permissions

Figure 6

Experimental and theoretical $\mathit{dI}/\mathit{dV}$ map of the molecule recorded at the energy of the HOMO-1, HOMO, and LUMO of the system for zero, one, and two atoms interacting with the molecule. A good agreement is seen between experiment and theory. Experimental and theoretical images shows how approaching one atom in the vicinity of the molecule deforms nonlocally its molecular orbitals due to their delocalization over the molecular board.Reuse & Permissions

Figure 7

$\mathit{dI}/\mathit{dV}$ spectra for the three nonequivalent Au-trinaphthylene molecule configurations. While a broad peak corresponding to the LUMO appears in all configurations at the positive bias, a distinct peak in the negative regime observed on a bare molecule is split and shifted by Au atom inputs. The HOMO of a molecule in gas phase, with a threefold symmetry, and the degenerated HOMO-1 and HOMO-2 orbitals, with twofold and mirror symmetries, are very close to the same energy level. However once adsorbed on a substrate this degeneracy unravels due to symmetry constrains resulting in the HOMO-2 orbital being dropped out from this energy range. Therefore the peak at $-$1600 mV in the spectrum taken from a bare molecule consists of only HOMO and HOMO-1. The surface state of Au(111) is provided as a reference.Reuse & Permissions

Figure 8

$I-V$ characteristics recorded by positioning the tip apex at the output side of the molecule exactly at the maximum lobe position of the first resonance at negative bias voltage (HOMO). Four $I-V$ characteristics were recorded corresponding to 0, 1, 1, and 2 Au input atoms at the in position. The absolute value of the current intensity is larger in the (0,0) case than in the three other case which is the requirement to obtain a NOR gate.Reuse & Permissions

Figure 9

The molecular orbital diagrams of the trinaphthylene molecule for the three different input configurations calculated using the PM6 method. Connecting a Au atom with the molecule deforms its molecular orbitals.Reuse & Permissions

Figure 10

Energy correlation diagram for the ground (1A1) and first excited states of the molecule. Notice how for energies up to the Fermi level the Au interaction spreads the monoelectronic excitation states, many of them being uncoupled from the surface and the tip in an STM junction.Reuse & Permissions