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Register a new userBasic concepts in single-molecule electronics
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C J Lambert
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This tutorial outlines the basic theoretical concepts and tools which underpin the fundamentals of phase-coherent electron transport through single molecules. The key quantity of interest is the transmission coefficient T(E), which yields the electrical conductance, current-voltage relations, the thermopower S and the thermoelectric figure of merit ZT of single-molecule devices. Since T(E) is strongly affected by quantum interference (QI), three manifestations of QI in single-molecules are discussed, namely Mach-Zehnder interferometry, Breit-Wigner resonances and Fano resonances. A simple MATLAB code is provided, which allows the novice reader to explore QI in multi-branched structures described by a tight-binding (Huckel) Hamiltonian. More generally, the strengths and limitations of materials-specific transport modelling based on density functional theory are discussed.
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Topological insulators are a new class of materials that have attracted significant attention in contemporary condensed matter physics. They are different from the regular insulators and they display novel quantum properties that also involve the idea of `topology, an area of mathematics. Some of the fundamental ideas behind the topological insulators, particularly in low-dimensional condensed matter systems such as poly-acetylene chains, can be understood using a simple one-dimensional toy model popularly known as the Su-Schrieffer-Heeger model or the SSH model. This model can also be used as an introduction to the topological insulators of higher dimensions. Here we give a concise description of the SSH model along with a brief review of the background physics and attempt to understand the ideas of topological invariants, edge states, and bulk-boundary correspondence using the model.
We present a general analytical formula and an ab initio study of quantum interference in multi-branch molecules. Ab initio calculations are used to investigate quantum interference in a benzene-1,2-dithiolate (BDT) molecule sandwiched between gold electrodes and through oligoynes of various lengths. We show that when a point charge is located in the plane of a BDT molecule and its position varied, the electrical conductance exhibits a clear interference effect, whereas when the charge approaches a BDT molecule along a line normal to the plane of the molecule and passing through the centre of the phenyl ring, interference effects are negligible. In the case of olygoynes, quantum interference leads to the appearance of a critical energy $E_c$, at which the electron transmission coefficient $T(E)$ of chains with even or odd numbers of atoms is independent of length. To illustrate the underlying physics, we derive a general analytical formula for electron transport through multi-branch structures and demonstrate the versatility of the formula by comparing it with the above ab-initio simulations. We also employ the analytical formula to investigate the current inside the molecule and demonstrate that large counter currents can occur within a ring-like molecule such as BDT, when the point charge is located in the plane of the molecule. The formula can be used to describe quantum interference and Fano resonances in structures with branches containing arbitrary elastic scattering regions connected to nodal sites.
This mini review focuses on conductance measurements through molecular junctions containing few tens of molecules, which are fabricated along two approaches: (i) conducting atomic force microscope contacting a self-assembled monolayers on metal surface, and (ii) tiny molecular junctions made of metal nanodot (diameter < 10 nm), covered by fewer than 100 molecules and contacted by a conducting atomic force microscope. In particular, this latter approach has allowed to obtain new results or to revisit previous ones, which are reviewed here: (i) how the electron transport properties of molecular junctions are modified by mechanical constraint, (ii) the role of intermolecular interactions on the shape of conductance histograms of molecular junctions, and (iii) the demonstration that a molecular diode can operate in the microwave regime up to 18 GHz.
We have used the electromigration technique to fabricate a $rm{C_{{60}}}$ single-molecule transistor (SMT). We present a full experimental study as a function of temperature, down to 35 mK, and as a function of magnetic field up to 8 T in a SMT with odd number of electrons, where the usual spin-1/2 Kondo effect occurs, with good agreement with theory. In the case of even number of electrons, a low temperature magneto-transport study is provided, which demonstrates a Zeeman splitting of the zero-bias anomaly at energies well below the Kondo scale.
Electronic transport properties for single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions or by means of scanning tunneling microscopes. In parallel, many theoretical tools have been developed and refined for describing such transport properties and for obtaining numerical predictions. Most prominent among these theoretical tools are those based upon density functional theory. In this review, theory and experiment are critically compared and this confrontation leads to several important conclusions. The theoretically predicted trends nowadays reproduce the experimental findings quite well for series of molecules with a single well-defined control parameter, such as the length of the molecules. The quantitative agreement between theory and experiment usually is less convincing, however. Many reasons for quantitative discrepancies can be identified, from which one may decide that qualitative agreement is the best one may expect with present modeling tools. For further progress, benchmark systems are required that are sufficiently well-defined by experiment to allow quantitative testing of the approximation schemes underlying the theoretical modeling. Several key experiments can be identified suggesting that the present description may even be qualitatively incomplete in some cases. Such key experimental observations and their current models are also discussed here, leading to several suggestions for extensions of the models towards including dynamic image charges, electron correlations, and polaron formation.
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