A quantum circuit rule for interference effects in single-molecule electrical junctions

Abstract

A quantum circuit rule for combining quantum interference effects in the conductive properties of oligo(phenyleneethynylene) (OPE)-type molecules possessing three aromatic rings was investigated both experimentally and theoretically. Molecules were of the type X-Y-X, where X represents pyridyl anchors with para (p), meta (m) or ortho (o) connectivities and Y represents a phenyl ring with p and m connectivities. The conductances G XmX (G XpX ) of molecules of the form X-m-X (X-p-X), with meta (para) connections in the central ring, were predominantly lower (higher), irrespective of the meta, para or ortho nature of the anchor groups X, demonstrating that conductance is dominated by the nature of quantum interference in the central ring Y. The single-molecule conductances were found to satisfy the quantum circuit rule G ppp /G pmp ¼ G mpm /G mmm . This demonstrates that the contribution to the conductance from the central ring is independent of the para versus meta nature of the anchor groups. S tudies of the electrical conductance of single molecules attached to metallic electrodes not only probe the fundamentals of quantum transport but also provide the knowledge needed to develop future molecular-scale devices and functioning circuits [1][2][3][4][5][6][7][8][9] . Owing to their small size (on the scale of Angstroms) and the large energy gaps (on the scale of eV), transport through single molecules can remain phase coherent even at room temperature, and constructive or destructive quantum interference (QI) can be utilized to manipulate their room temperature electrical 10-13 and thermoelectrical 14,15 properties. In previous studies, it was reported theoretically and experimentally that the conductance of a phenyl ring with meta (m) connectivity is lower than the isomer with para (p) connectivity by several orders of magnitude [16][17][18][19][20][21][22][23][24][25] . This arises because partial de Broglie waves traversing different paths through the ring are perfectly out of phase leading to destructive QI in the case of meta coupling, while for para or ortho coupling they are perfectly in phase and exhibit constructive QI. (See, for example, equation 8 of ref. 26.) It is therefore natural to investigate how QI in molecules with multiple aromatic rings can be utilized in the design of more complicated networks of interference-controlled molecular units.The basic unit for studying QI in single molecules is the phenyl ring, with thiol 17,21 , methyl thioether 27 , amine 17 or cyanide 19 anchors directly connecting the aromatic ring to gold electrodes. Recently, Arroyo et al. 28,29 studied the effect of QI in a central phenyl ring by varying the coupling to various anchor groups, including two variants of thienyl anchors. However, the relative importance of QI in central rings compared with QI in anchor groups has not been studied systematically because the thienyl anchors of Arroyo et al. 28,29 were five-membered rings, which exhibit only constructive interference. To study the relative effect of QI in anchors,...

Gating of Quantum Interference in Molecular Junctions by Heteroatom Substitution

“…0.8 nm (after adding the snap back distance of 0.5 nm it will be 1.3 nm), suggesting that the most pronouncing feature stems from the molecules trapped only via Au−S bonds. However, the 2D histograms of the meta ‐coupled molecules (Figure S9, SI) show that the conductance cloud becomes less clear as previously reported in the literature 4d, 13. Apparently, the bent molecular geometry strongly affects the evolution of molecular junctions, resulting in a slanted conductance region.…”

Using coherence to enhance function in chemical and biophysical systems

“…These observations contrast with predictions from circuit analogues where resistors are wired in parallel 23 . A similar partitioning of ortho/para versus meta pathways is well known in synthetic chemistry, and is widely exploited in electrophilic aromatic substitution reactions.…”

“…Adding wave amplitudes, or interference phenomena, has dramatic consequences. For example, when a molecule spans two electrodes 20,21 transport junctions form, revealing striking differences in current according to the interference of the pathways by which electrons can be routed through a molecule 22,23 . As the electron tunnels through the molecule it traverses physical, structural pathways according to the amplitudes and energies of molecular orbitals [24][25][26] .…”

Destructive quantum interference in electron transport: A reconciliation of the molecular orbital and the atomic orbital perspective

“…1. Therefore, for the purpose of device design the molecular contribution can be optimized independently from the coupling to the metal contacts, a notion which has been recently confirmed in a joint theoretical and experimental work by Manrique et al 26 . In this study it was shown that molecules and even their fragments contribute well defined and transferable factors to electron transport as a crucial observation for the investigation of destructive quantum interference (DQI) effects, a phenomenon which has been the topic of a tremendous number of recent articles, where for a rather complete bibliography we refer to Ref.…”