Searching the Hearts of Graphene-like Molecules for Simplicity, Sensitivity, and Logic

Abstract

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons could be isolated and manipulated, then a significant step toward realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene, or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers.

Quantum interference and heteroaromaticity of para- and meta-linked bridged biphenyl units in single molecular conductance measurements

“…Several studies have established that para (conjugated) connectivity through a core unit results in enhanced conductance compared to the isomeric meta (reduced conjugation) connectivity. This is ascribed to quantum interference and has been observed experimentally and theoretically in aromatic rings such as benzene 26–29 , naphthalene 14 , anthracene 14 , pyrene 30 and anthanthrene 31 .…”

“…Since the latter is a bipartite lattice, in the meta case, destructive interference should occur at the centre of the HOMO–LUMO gap (i.e. E  = 0) 11, 30, 31 . The black curves in Fig.…”

Distinguishing Lead and Molecule States in Graphene-Based Single-Electron Transistors

“…In this expression, the scatterering region is a complex combination of the molecule and graphene and G SS is the Green’s function of the scattering region in the presence of the simple crystalline leads. Our aim is to separate the contributions to scattering from the molecule and graphene and therefore we adopt an alternative formulation 20 in which the left graphene, and left semi-infinite lead, i.e., the region n < 0, are regarded as a compound electrode (L) and the right graphene and right semi-infinite lead ( n > 0) form the right compound electrode (R). This viewpoint is encapsulated in the following alternative expression for the transmission coefficient, which is mathematically equivalent to eq 4In this equation, the level broadening due to contact between the molecule and the left and right compound electrodes are described bywhere g LL(RR) is the Green’s function of the isolated left(right)-hand compound electrode, and H L(R)M denotes the coupling between the left(right) compound electrode and the molecule.…”

Gating of Quantum Interference in Molecular Junctions by Heteroatom Substitution

“…The accuracy of the MRR for polycyclic aromatic hydrocarbons (PAHs) is demonstrated in Ref. 8b, in which MRR predictions for the ratios of conductances for a range of PAHs are compared with experiments. A remarkable feature of the MRR is that the associated most‐probable conductance ratios are independent of the binding geometry, elongation etc., even though the conductances themselves do depend on such features.…”