Thermoelectric Enhancement of Series-Connected Cross-Conjugated Molecular Junctions

TL;DR

The paper addresses scalable enhancement of thermoelectric response in single-molecule junctions by exploiting quantum interference in series-connected, node-bearing backbones. It develops a nonequilibrium quantum transport framework with a two-stage Lanczos-based Green's function evaluation for the many-body pi-system, and demonstrates that adding repeat units increases nodal density while keeping the electronic gap fixed. A low-energy split-node model predicts robust, significant boosts in Seebeck coefficient $|S|$, electronic figure of merit $ZT_{\rm e}$, and maximum efficiency $\eta_{\max}/\eta_C$ as a function of chain length, and shows split-nodes can outperform ideal supernodes under realistic conditions. The practical design principles include optimizing node spacing around $\Delta_{\rm peak}\approx 3.4$–$3.5\,k_B T_0$ and suppressing $\sigma$-channel leakage, with iso-PDA scaffolds and end-group engineering highlighted as viable routes toward device-scale quantum-enhanced thermoelectrics.

Abstract

We investigate the thermoelectric response of single-molecule junctions composed of acyclic cross-conjugated molecules, including dendralene analogues and related iso-poly(diacetylene) (iso-PDA) motifs, in which node-possessing repeat units are connected in series. Using many-body quantum transport theory, we show that increasing the number of repeat units leaves the fundamental gap essentially unchanged while giving rise to a split-node spectrum whose cumulative broadening dramatically enhances the thermopower. This form of quantum enhancement can exceed other interference-based mechanisms, such as the coalescence of nodes into a supernode, suggesting new opportunities for scalable quantum-interference-based materials. Although illustrated here with cross-conjugated systems, the underlying principles apply broadly to series-connected architectures hosting multiple interference nodes. Finally, we evaluate the scaling of the electronic figure of merit ZT and the maximum thermodynamic efficiency. Together, these results highlight the potential for split-node-based materials to realize quantum-enhanced thermoelectric response.

Figures (5)

• Figure S1: Schematic diagrams of thiolated, alkynyl-extended iso-poly(acetylene) (top) and iso-poly(diacetylene) (bottom) analogues, denoted NCC and NCCA, respectively. Each cross-conjugated repeat unit contains terminal "stub" C--C groups with substituents $R$. In principle, these may be varied to stabilize the backbone or tune onsite energies. In this work, we set $R=H$ to isolate the intrinsic interference features.
• Figure S2: Many-body calculated transmission probability $\mathcal{T}_\pi$ and conductance $G_\pi$ (left panels) and total thermopower $S$ (right panels) for NCC junctions with $N$ = 1--4, shown as a function of electrode chemical potential $\mu$. The mid-gap energy is set to zero in all cases. Each repeated unit introduces one quadratic transmission node, so the total number of nodes equals $N$, while the fundamental gap remains nearly independent of $N$. The HOMO and LUMO features near $\pm 4$ eV correspond to the many-body addition/removal resonances ($N-1 \to N$ and $N \to N+1$ charging excitations) of the $\pi$-system, rather than Kohn–Sham orbital levels. The nearly constant gap reflects the repeat-unit conjugation length, not the overall molecular size. Black lines in the left panels show the $\sigma$-channel background ($\mathcal{T}_\sigma$ with $\beta_\sigma =$ 1 Å$^{-1}$, $A_\sigma=10^{-4}$), included to illustrate how even a small energy-independent $\sigma$ contribution can obscure $\pi$-system variations. The thermopower exhibits sharp peaks near each node, normalized to the quadratic-node value $S_0=\pi/\sqrt{3}\,(k_B/e) \approx 156$$\upmu$V/K. As $N$ increases, overlapping tails of adjacent peaks enhance the mid-gap response. Dashed lines show results with nonzero $\mathcal{T}_\sigma$, which wash out the interference-induced thermopower enhancement. Conductance is normalized to the quantum $G_0=2$e$^2$/h. Calculations correspond to room temperature, $T_0=300$ K.
• Figure S3: Many-body calculated total $ZT_{\rm e}$ (left panels) and total normalized maximum efficiency $\eta_{\rm max}/\eta_{\rm C}$ (right panels) for NCC junctions with $N$ = 1--4. In 1CC, the mid-gap node is strongly affected by $\sigma$ leakage, with peak $ZT_{\rm e}$ reduced from $\sim$0.75 to $\sim$0.21. For 2CC, the split nodes lie nearer the frontier resonances, and the suppression is lessened ($\sim$0.96 to $\sim$0.61). In 3CC, the central mid-gap node collapses ($\sim$0.75 to $\sim$0.022), but the side nodes retain large values ($\sim$1.25 to $\sim$1.06). By 4CC, additional nodes crowd the resonance regions, yielding near-resonant peaks exceeding 1.5 that remain largely insensitive to $\sigma$ transport. $\sigma$-channel transport is estimated using $\beta_\sigma=1.0$ Å, and $A_\sigma$ = $10^{-4}$. All calculations correspond to $T_0=300$ K.
• Figure S4: Many-body calculated transmission $\mathcal{T}$ and conductance $G$ (left panels) and thermopower $S$ (right panels) for NCCA junctions with $N=1$--3, shown as functions of electrode chemical potential $\mu$ (mid-gap set to zero). Each repeat unit introduces a transmission node, while the fundamental gap remains nearly independent of $N$, though slightly reduced relative to the NCC series. The longer saturated backbones of the NCCs suppress the $\sigma$-channel background, as illustrated by the black lines in the left panels ($A_\sigma=10^{-4}$, $\beta_\sigma=1.0$), thereby preserving the $\pi$-system interference pattern and allowing the nodal thermopower enhancement to emerge more clearly than in Figure \ref{['fig:NCC']}. Conductance is normalized to the quantum $G_0=2$e$^2$/h, thermopower to the quadratic-node peak value $S_0=\pi/\sqrt{3}\,(k_B/e)$, and all calculations correspond to room temperature ($T_0=300$ K).
• Figure S5: Maximum thermopower $|S|$, electronic figure of merit $ZT_{\rm e}$, and normalized maximum efficiency $\eta_{\max}/\eta_{\rm C}$ obtained from the split-node model of Equation (\ref{['eq:Tmodel']}). The left panel shows each quantity as a function of node spacing $\Delta/(k_B T_0)$ for several chain lengths $N$, while the right panel shows the global maxima of the same quantities as a function of $N$ with ${\cal T}_\sigma=0$. In all cases, the optimum occurs at $\Delta/(k_B T_0)\simeq 3.4$--$3.5$, essentially independent of $N$, whereas the attainable maxima increase systematically with molecular length. (The $\Delta=0$ limit corresponds to the supernode case). The green and blue vertical lines correspond to the peak splitting for $S$ and $ZT$, respectively. The relative enhancement of split-node junctions over the supernode grows further with $N$, highlighting the parameter window where series-connected, node-bearing architectures can outperform the supernode limit.