Many-Body Effects in a Molecular Quantum NAND Tree

TL;DR

This work shows that chemically encoded NAND gates can be realized in single-molecule junctions using quantum interference, with inputs set by end-group substitutions on alkynyl-extended iso-polyacetylene backbones. It develops a robust many-body transport framework (MDE/NEGF) to incorporate dynamical electron correlations, revealing that while NAND behavior persists, nodal energies and substitution trends shift due to correlations. Thermopower emerges as a chemically robust readout for the gate state, offering large discrimination margins even when conductance signals are obscured by contact details or sigma-channel background. The results highlight correlations as a design parameter that can reshape or generate transmission nodes, extending molecular logic into the many-body Fock space and suggesting pathways toward interaction-enabled molecular computation with practical readout strategies.

Abstract

Molecules provide the smallest possible circuits in which quantum interference and electron correlation can be engineered to perform logical operations, including the universal NAND gate. We investigate a chemically encoded quantum NAND tree based on alkynyl-extended iso-polyacetylene backbones, where inputs are set by end-group substitution and outputs are read from the presence or absence of transmission nodes. Using quantum many-body transport theory, we show that NAND behavior persists in the presence of dynamic correlations, but that the nodal positions and their chemical shifts depend sensitively on electron-electron interactions. This sensitivity highlights the potential of these systems not only to probe the strength of electronic correlations but also to harness them in shaping logical response. The thermopower is identified as a chemically robust readout of gate logic, providing discrimination margins that greatly exceed typical experimental uncertainties, in an observable governed primarily by the variation of transport rather than its absolute magnitude.

Figures (9)

• Figure S1: (a) Schematic representation of a single-level NAND stub, illustrating the four possible input combinations and their logical outputs. Inputs are encoded as branches labeled 0 (blue) or 1 (magenta), with the NAND truth table reproduced by the transmission response at the nodal energy. (b) Molecular realizations based on thiolated, alkynyl-extended iso-poly(acetylene) (iso-PA) backbones. Logical $0$ is represented by an NH2 substituent, while logical $1$ is represented by a vinyl (C=C) group. Outputs are read from the transmission spectrum near the nodal energy, as obtained in transport measurements when macroscopic Au electrodes are coupled to the terminal thiol groups.
• Figure : (a) Single-particle tight-binding theory
• Figure S3: Transmission $\mathcal{T}_\pi$, conductance $G$, and thermopower $S$ for NAND junctions computed within the many-body MDE theory including only local Coulomb interactions ($U_{nm} = \delta_{nm}$9.69 eV, i.e. the Hubbard model). As in Fig. \ref{['fig:NAND_thermo_manybody']}, the $(0,1)$ and $(1,0)$ inputs yield identical transport owing to molecular symmetry. Energies are referenced to the effective carbon onsite potential, and a weak $\sigma$-channel background is shown for comparison. Relative to the independent-electron (Hückel) case, both the Hubbard and long-range Coulomb descriptions predict that the $(0,0)$ and $(1,0)$ nodes shift downward in energy, underscoring the role of electronic correlation. The Hubbard model further restores nearly uniform nodal separations while retaining the overall energetic trends of the full Coulomb calculation, illustrating the distinct influences of local versus nonlocal interactions on logical response. Conductance is normalized to $G_0 = 2e^2/h$ and calculations correspond to $T_0=300$ K.
• Figure : (a) Single-particle theory
• Figure : (a) Single-particle tight-binding theory