We predict an enormous order-dependent quantum enhancement of thermoelectric effects in the vicinity of a higher-order 'supernode' in the transmission spectrum of a nanoscale junction. Singlemolecule junctions based on 3,3'-biphenyl and polyphenyl ether (PPE) are investigated in detail. The nonequilibrium thermodynamic efficiency and power output of a thermoelectric heat engine based on a 1,3-benzene junction are calculated using many-body theory, and compared to the predictions of the figure-of-merit ZT .Thermoelectric (TE) devices are highly desirable since they can directly convert between thermal and electrical energy. Electrical power can be supplied to such a device to either heat or cool adjoining reservoirs (Peltier effect) or alternatively, the flow of heat (e.g. from a factory or car exhaust) can be converted into usable electrical power (Seebeck effect). Often, the efficiency of a TE device is characterized by the dimensionless figure-of-merit ZT =S 2 GT /κ, constructed with the rationale that an efficient TE device should simultaneously: maximize the electrical conductance G so that current can flow without much Joule heating, minimize the thermal conductance κ in order to maintain a temperature gradient across the device, and maximize the Seebeck coefficient S to ensure that the coupling between the electronic and thermal currents is as large as possible.1,2 Generally, however, ZT is difficult to maximize because these properties are highly correlated with one another, 3-5 a fact that becomes more pronounced at the nanoscale where the number of degrees of freedom available is small.If a TE material were found exhibiting ZT ≥4 it would constitute a commercially viable solution for many heating and cooling problems at both the macro-and nanoscales, with no operational carbon footprint.2 Currently, the best TE materials available in the laboratory exhibit ZT ≈3, whereas for commercially available TE devices ZT ≈1, owing to various packaging and fabrication challenges. 1,6In a previous article, enhanced thermoelectric effects were found in the vicinity of a transmission node of a quantum tunneling device. Generically, the transmission probability vanishes quadratically as a function of energy at such a transmission node.7 Here we present results for a class of two-terminal single-molecule junctions (SMJ) with higher-order 'supernodes' in their transmission spectra. In the vicinity of a 2n th order supernode:where µ node is the energy of the node. We find that junctions possessing such supernodes exhibit a scalable orderdependent quantum-enhanced thermoelectric response.As an example, ZT of a supernode-possessing polyphenyl ether (PPE)-based SMJ is shown as a function of repeated phenyl unit number n in Fig. (1). As illustrated in the figure, ZT peak scales super-linearly in n whereby ZT peak =4.1 in a junction composed of just four phenyl groups (n=4). Although we focus on molecular junctions in this article, it should be stressed that our results are applicable to any device with transmission nodes ari...

An exact expression for the heat current in an interacting nanostructure is derived and used to calculate the thermoelectric response of three representative single-molecule junctions formed from isoprene, 1,3-benzenedithiol, and [18]-annulene. Dramatic enhancements of the thermopower S and Lorenz number L are predicted when the junction is tuned across a node in the transmission function, with universal maximum values S(max) = (pi/3(1/2))(k(B)/e) and L(max) = (7pi(2)/5)(k(B)(2)/e(2)). The effect of a finite minimum transmission probability due, e.g., to incoherent processes or additional nonresonant channels, is also considered.

A many-body theory of molecular junction transport based on nonequilibrium Green's functions is developed, which treats coherent quantum effects and Coulomb interactions on an equal footing. The central quantity of the many-body theory is the Coulomb self-energy matrix ΣC of the junction. ΣC is evaluated exactly in the sequential tunneling limit, and the correction due to finite tunneling width is evaluated self-consistently using a conserving approximation based on diagrammatic perturbation theory on the Keldysh contour. Our approach reproduces the key features of both the Coulomb blockade and coherent transport regimes simultaneously in a single unified transport theory. As a first application of our theory, we have calculated the thermoelectric power and differential conductance spectrum of a benzenedithiol-gold junction using a semi-empirical π-electron Hamiltonian that accurately describes the full spectrum of electronic excitations of the molecule up to 8-10eV.

Transport through an Anderson junction (two macroscopic electrodes coupled to an Anderson impurity) is dominated by a Kondo peak in the spectral function at zero temperature. We show that the single-particle Kohn-Sham potential of density-functional theory reproduces the linear transport, despite the lack of a Kondo peak in its spectral function. Using Bethe ansatz techniques, we calculate this potential for all coupling strengths, including the crossover from mean-field behavior to charge quantization caused by the derivative discontinuity. A simple and accurate interpolation formula is also given.

A precise definition for a quantum electron thermometer is given, as an electron reservoir coupled locally (e.g., by tunneling) to a sample, and brought into electrical and thermal equilibrium with it. A realistic model of a scanning thermal microscope with atomic resolution is then developed, including the effect of thermal coupling of the probe to the ambient environment. We show that the temperatures of individual atomic orbitals or bonds in a conjugated molecule with a temperature gradient across it exhibit quantum oscillations, whose origin can be traced to a realization of Maxwell's demon at the single-molecule level. These oscillations may be understood in terms of the rules of covalence describing bonding in π-electron systems. Fourier's law of heat conduction is recovered as the resolution of the temperature probe is reduced, indicating that the macroscopic law emerges as a consequence of coarse graining.

We investigate electronic transport through molecular radicals and predict a correlation-induced transmission node arising from destructive interference between transport contributions from different charge states of the molecule. This quantum interference effect has no single-particle analog and cannot be described by effective single-particle theories. Large errors in the thermoelectric properties and nonlinear current-voltage response of molecular radical junctions are introduced when the complementary wave and particle aspects of the electron are not properly treated. A method to accurately calculate the low-energy transport through a radical-based junction using an Anderson model is given.

We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe (i) is independent of details of the system-probe coupling, (ii) is equal to the temperature obtained from an independent current-noise measurement, (iii) satisfies the transitivity condition expressed by the zeroth law of thermodynamics, and (iv) is consistent with Carnot's theorem. This local temperature therefore characterizes the system in the common sense of equilibrium thermodynamics, but remains well defined even in out-of-equilibrium situations with no local equilibrium.

The “Quo Vadis?” meeting in Bremen (March 2013) was a spectacular opportunity for people involved in molecular electronics to catch up on the latest, to think back, and to project into the future. This manuscript is divided into two halves. In the first half, we address some of the history and where the field has advanced in the areas of measuring, modeling, making, and understanding materials. We review some big ideas that have animated the field of molecular electronics since its beginning, and are at the height of interest and accomplishment at the moment. Then, we discuss six major areas where the field is evolving, and in which we expect to see very exciting work in the years and decades ahead. As a representative of one of the neer themes, the second half of the paper is devoted to molecular thermoelectrics. It contains some formalism, some results, some experimental comparison, and some intriguing conceptual questions, both for pure science and for device applications. An artist's rendition of a self‐assembled monolayer of polyphenylether molecules on Au contacted by a Au STM.