Author Correction: Gate controlling of quantum interference and direct observation of anti-resonances in single molecule charge transport.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Deep-Learning Approach to First-Principles Transport Simulations.

Large-scale first-principles transport calculations, while essential for device modeling, remain computationally demanding. To overcome this bottle neck, we combine first-principles transport calculations with machine learning-based nonlinear regression. We calculate the electronic conductance through first-principles based nonequilibrium Green's function techniques for small systems and map the transport properties onto local properties using local descriptors. We show that using the local descriptor as input features for deep learning-based nonlinear regression allows us to build a robust neural network that can predict the conductance of large systems beyond that of the current state-of-the-art first-principles calculation algorithms. Our protocol is applied to alkali metal nanowires, i.e., potassium, which have unique geometrical and electronic properties and hence nontrivial transport properties. We demonstrate that within our approach we can achieve qualitative agreement with experiment at a fraction of the computational effort as compared to the direct calculation of the transport properties using conventional first-principles methods.

Gate controlling of quantum interference and direct observation of anti-resonances in single molecule charge transport.

Quantum interference can profoundly affect charge transport in single molecules, but experiments can usually measure only the conductance at the Fermi energy. Because, in general, the most pronounced features of the quantum interference are not located at the Fermi energy, it is highly desirable to probe charge transport in a broader energy range. Here, by means of electrochemical gating, we measure the conductance and map the transmission functions of single molecules at and around the Fermi energy, and study signatures associated with constructive and destructive interference. With electrochemical gate control, we tune the quantum interference between the highest occupied molecular orbital and lowest unoccupied molecular orbital, and directly observe anti-resonance, a distinct feature of destructive interference. By tuning the molecule in and out of anti-resonance, we achieve continuous control of the conductance over two orders of magnitude with a subthreshold swing of ~17 mV dec-1, features relevant to high-speed and low-power electronics.

How To Probe the Limits of the Wiedemann-Franz Law at Nanoscale.

While the Wiedemann-Franz law is known to be robust for many bulk materials, possible violations have been actively discussed for certain classes of bulk materials such as heavy Fermion materials. At nanoscale on the other hand the limits of the Wiedemann-Franz law and how to probe and control them remains an open question. Therefore, we propose here a systematic way to elucidate the limits of the Wiedemann-Franz law at nanoscale. Using first-principles calculations, we examine the Wiedemann-Franz law in nanoscale conductors, namely in gold and platinum-based atomic wires. We explain the recently observed experimental evidence of the Wiedemann-Franz law in atomic-point contacts, but conversely we show that in regimes not discussed in these experiments notable violations of the Wiedemann-Franz law emerge. Depending on the temperature and gate potential as well as chemical properties and conformation, the violations reach up to 30% for gold and for platinum they can even exceed 350%.

The Orbital Selection Rule for Molecular Conductance as Manifested in Tetraphenyl-Based Molecular Junctions.

Using two tetraphenylbenzene isomers differing only by the anchoring points to the gold electrodes, we investigate the influence of quantum interference on the single molecule charge transport. The distinct anchor points are realized by selective halogen-mediated binding to the electrodes by formation of surface-stabilized isomers after iodine cleavage. Both isomers are essentially chemically identical and only weakly perturbed by the electrodes avoiding largely parasitic effects, which allows us to focus solely on the relation between quantum interference and the intrinsic molecular properties. The conductance of the two isomers differs by over 1 order of magnitude and is attributed to constructive and destructive interference. Our ab initio based transport calculations compare very well with the accompanying scanning tunneling microscope break junction measurements of the conductance. The findings are rationalized using a two level model, which shows that the interorbital coupling plays the decisive role for the interference effects.

Competitive effects of oxygen vacancy formation and interfacial oxidation on an ultra-thin HfO2-based resistive switching memory: beyond filament and charge hopping models.

We studied the quantum transport mechanism of an ultra-thin HfO2-based resistive random access memory (ReRAM) cell with TiN electrodes and proposed the design of a sub-10 nm scale device. It is believed that formation and rupture of the conduction path in the local filament causes the switching between high and low resistive states. However, the validity of this simple filament model is not obvious in the sub-10 nm scale device because the redox processes occur mainly in a few nm range at the interface. Furthermore, the intrinsic transport mechanism of the device, in particular, quantum coherence, depends on device materials and length-scale. The relationship between the redox states and the transport mechanism like ballistic or hopping is still under debate when the device length scale is less than 10 nm. In the present study, we performed first-principles calculations of the non-equilibrium Green's function including electron-phonon interactions. We examined several characteristic structures of the HfO(x) wire (nano-scale conduction path) and the interfaces between the resistive switching layer and electrodes. We found that the metal buffer layer induced a change in the oxygen-reduction site from the interface of HfO(x)/TiN to the buffer layer. Even when the inserted buffer layer is a few atomic layers, this effect plays an important role in the enhancement of the performance of ON/OFF resistive switching and in the reduction of the inelastic electric current by electron-phonon scattering. The latter suppresses the hopping mechanism, which makes the ballistic conduction the dominant mechanism. We evaluated the activation energy in the high temperature limit by using the first-principles results of inelastic current. Our theoretical model explains the observed crossover of the temperature dependence of ReRAM cells and gives a new insight into the principle of operation on a sub-10 nm scale ReRAM device.

The effect of a Ta oxygen scavenger layer on HfO2-based resistive switching behavior: thermodynamic stability, electronic structure, and low-bias transport.

Reversible resistive switching between high-resistance and low-resistance states in metal-oxide-metal heterostructures makes them very interesting for applications in random access memories. While recent experimental work has shown that inserting a metallic "oxygen scavenger layer" between the positive electrode and oxide improves device performance, the fundamental understanding of how the scavenger layer modifies the heterostructure properties is lacking. We use density functional theory to calculate thermodynamic properties and conductance of TiN/HfO2/TiN heterostructures with and without a Ta scavenger layer. First, we show that Ta insertion lowers the formation energy of low-resistance states. Second, while the Ta scavenger layer reduces the Schottky barrier height in the high-resistance state by modifying the interface charge at the oxide-electrode interface, the heterostructure maintains a high resistance ratio between high- and low-resistance states. Finally, we show that the low-bias conductance of device on-states becomes much less sensitive to the spatial distribution of oxygen removed from the HfO2 in the presence of the Ta layer. By providing a fundamental understanding of the observed improvements with scavenger layers, we open a path to engineer interfaces with oxygen scavenger layers to control and enhance device performance. In turn, this may enable the realization of a non-volatile low-power memory technology with concomitant reduction in energy consumption by consumer electronics and offering significant benefits to society.

Toward Multiple Conductance Pathways with Heterocycle-Based Oligo(phenyleneethynylene) Derivatives.

In this paper, we have systematically studied how the replacement of a benzene ring by a heterocyclic compound in oligo(phenyleneethynylene) (OPE) derivatives affects the conductance of a molecular wire using the scanning tunneling microscope-based break junction technique. We describe for the first time how OPE derivatives with a central pyrimidine ring can efficiently link to the gold electrode by two pathways presenting two different conductance G values. We have demonstrated that this effect is associated with the presence of two efficient conductive pathways of different length: the conventional end-to-end configuration, and another with one of the electrodes linked directly to the central ring. This represents one of the few examples in which two defined conductive states can be set up in a single molecule without the aid of an external stimulus. Moreover, we have observed that the conductance through the full length of the heterocycle-based OPEs is basically unaffected by the presence of the heterocycle. All these results and the simplicity of the proposed molecules push forward the development of compounds with multiple conductance pathways, which would be a breakthrough in the field of molecular electronics.

Single-molecule conductance of a chemically modified, π-extended tetrathiafulvalene and its charge-transfer complex with F4TCNQ.

We describe the synthesis and single-molecule electrical transport properties of a molecular wire containing a π-extended tetrathiafulvalene (exTTF) group and its charge-transfer complex with F4TCNQ. We form single-molecule junctions using the in situ break junction technique using a homebuilt scanning tunneling microscope with a range of conductance between 10 G0 down to 10(-7) G0. Within this range we do not observe a clear conductance signature of the neutral parent molecule, suggesting either that its conductance is too low or that it does not form a stable junction. Conversely, we do find a clear conductance signature in the experiments carried out on the charge-transfer complex. Due to the fact we expected this species to have a higher conductance than the neutral molecule, we believe this supports the idea that the conductance of the neutral molecule is very low, below our measurement sensitivity. This idea is further supported by theoretical calculations. To the best of our knowledge, these are the first reported single-molecule conductance measurements on a molecular charge-transfer species.

Thermoelectric efficiency of organometallic complex wires via quantum resonance effect and long-range electric transport property.

Superior long-range electric transport has been observed in several organometallic wires. Here, we discuss the role of the metal center in the electric transport and examine the possibility of high thermoelectric figure of merit (ZT) by controlling the quantum resonance effects. We examined a few metal center (and metal-free) terpyridine-based complexes by first-principles calculations and clarified the role of the metals in determining the transport properties. Quasi-resonant tunneling is mediated by organic compounds, and narrow overlapping resonance states are formed when d-electron metal centers are incorporated. Distinct length (L) and temperature (T) dependencies of thermopower from semiconductor materials or organic molecular junctions are presented in terms of atomistic calculations of ZT with and without considering the phonon thermal conductance. We present an alternative approach to obtain high ZT for molecular junctions by quantum effect.

Controlling formation of single-molecule junctions by electrochemical reduction of diazonium terminal groups.

We report controlling the formation of single-molecule junctions by means of electrochemically reducing two axialdiazonium terminal groups on a molecule, thereby producing direct Au-C covalent bonds in situ between the molecule and gold electrodes. We report a yield enhancement in molecular junction formation as the electrochemical potential of both junction electrodes approach the reduction potential of the diazonium terminal groups. Step length analysis shows that the molecular junction is significantly more stable, and can be pulled over a longer distance than a comparable junction created with amine anchoring bonds. The stability of the junction is explained by the calculated lower binding energy associated with the direct Au-C bond compared with the Au-N bond.

Energy band structure calculations based on screened Hartree-Fock exchange method: Si, AlP, AlAs, GaP, and GaAs.

The screening effect on the Hartree-Fock (HF) exchange term plays a key role in the investigation of solid-state materials by first-principles electronic structure calculations. We recently proposed a novel screened HF exchange potential, in which the inverse of the dielectric constant represents the fraction of the HF exchange term incorporated into the potential. We demonstrated that this approach can be used to reproduce the energy band structure of diamond well [T. Shimazaki and Y. Asai, J. Chem. Phys. 130, 164702 (2009)]. In the present paper, we report that the screened HF exchange method is applicable to other semiconductors such as silicon, AlP, AlAs, GaP, and GaAs.

First principles band structure calculations based on self-consistent screened Hartree-Fock exchange potential.

A screened Hartree-Fock (HF) exchange potential with the dielectric constant was previously reported by Shimazaki and Asai [Chem. Phys. Lett. 466, 91 (2008)], in which the inverse of the dielectric constant was used to represent a fraction of the HF exchange term. In that report, the experimentally obtained value for the dielectric constant was employed. Herein, we discuss a self-consistent technique, in which the value of the dielectric constant can be automatically determined. This technique enables the energy band structure to be determined without using the experimental value. The band energy structure of diamond is calculated, a self-consistent procedure is determined to give closer bandgaps compared with the local density approximation and the generalized gradient approximation.

Thermal conductance of Teflon and Polyethylene: Insight from an atomistic, single-molecule level.

The thermal transport properties of teflon (polytetrafluoroethylene) and its polyethylene counterparts are, while highly desirable and widely used, only superficially understood. Here, we aim therefore to provide rigorous insight from an atomistic point of view in context of single-molecule devices. We show that for vinyl polymers adsorbed on metal-surfaces the thermal transport strongly depends on the properties of the metal-molecule interface and that the reduced thermal conductance observed for teflon derivatives originates in a reduced phonon injection life time. In asymmetric molecules phonon blocking on the intra molecular interface leads to a further reduction of thermal conductance. For hetrojunctions with different electrode materials we find that thermal conductance is suppressed due to a reduced overlap of the available phonon modes in the different electrodes. A detailed atomistic picture is thereby provided by studying the transport through perfluorooctane and octane on a single-molecule level using first principles transport calculations and nonequilibrium molecular dynamic simulations.

Resistive switching mechanism of GeTe-Sb2Te3 interfacial phase change memory and topological properties of embedded two-dimensional states.

A theoretical study of an interfacial phase change memory made of a GeTe-Sb2Te3 superlattice with W electrodes is presented to identify the high and low resistance states and the switching mechanism. The ferro structure of the GeTe layer block in the Te-Ge-Te-Ge sequence can be in the low resistance state only if the SET/RESET mode consists of a two step dynamical process, corresponding to a vertical flip of the Ge layer with respect to the Te layer, followed by lateral motion driven by thermal relaxation. The importance of spin-orbit coupling at the GeTe/Sb2Te3 interface to the "bias polarity-dependent" SET/RESET operation is shown, and an analysis of the two-dimensional states confined at the GeTe/Sb2Te3 interface inside the resistive switching layer is presented. Our results allow us to propose a phase diagram for the transition from a topologically nontrivial to a trivial gap state of these two-dimensional compounds.

Thermoelectric effect and its dependence on molecular length and sequence in single DNA molecules.

Studying the thermoelectric effect in DNA is important for unravelling charge transport mechanisms and for developing relevant applications of DNA molecules. Here we report a study of the thermoelectric effect in single DNA molecules. By varying the molecular length and sequence, we tune the charge transport in DNA to either a hopping- or tunnelling-dominated regimes. The thermoelectric effect is small and insensitive to the molecular length in the hopping regime. In contrast, the thermoelectric effect is large and sensitive to the length in the tunnelling regime. These findings indicate that one may control the thermoelectric effect in DNA by varying its sequence and length. We describe the experimental results in terms of hopping and tunnelling charge transport models.

Theoretical rate constants of super-exchange hole transfer and thermally induced hopping in DNA.

Recently, the electronic properties of DNA have been extensively studied, because its conductivity is important not only to the study of fundamental biological problems, but also in the development of molecular-sized electronics and biosensors. We have studied theoretically the reorganization energies, the activation energies, the electronic coupling matrix elements, and the rate constants of hole transfer in B-form double-helix DNA in water. To accommodate the effects of DNA nuclear motions, a subset of reaction coordinates for hole transfer was extracted from classical molecular dynamics (MD) trajectories of DNA in water and then used for ab initio quantum chemical calculations of electron coupling constants based on the generalized Mulliken-Hush model. A molecular mechanics (MM) method was used to determine the nuclear Franck-Condon factor. The rate constants for two types of mechanisms of hole transfer-the thermally induced hopping (TIH) and the super-exchange mechanisms-were determined based on Marcus theory. We found that the calculated matrix elements are strongly dependent on the conformations of the nucleobase pairs of hole-transferable DNA and extend over a wide range of values for the "rise" base-step parameter but cluster around a particular value for the "twist" parameter. The calculated activation energies are in good agreement with experimental results. Whereas the rate constant for the TIH mechanism is not dependent on the number of A-T nucleobase pairs that act as a bridge, the rate constant for the super-exchange process rapidly decreases when the length of the bridge increases. These characteristic trends in the calculated rate constants effectively reproduce those in the experimental data of Giese et al. [Nature 2001, 412, 318]. The calculated rate constants were also compared with the experimental results of Lewis et al. [Nature 2000, 406, 51].

Thermoelectricity at the molecular scale: a large Seebeck effect in endohedral metallofullerenes.

Single molecule devices provide a unique system to study the thermoelectric energy conversion at an atomistic level and can provide valuable information for the design of organic thermoelectric materials. Here we present a comprehensive study of the thermoelectric transport properties of molecular junctions based on C(82), Gd@C(82), and Ce@C(82). We combine precise scanning tunneling microscope break-junction measurements of the thermopower and conductance with quantitatively accurate self-energy-corrected first-principles transport calculations. We find that all three fullerene derivatives give rise to a negative thermopower (n-conducting). The absolute value, however, is much larger for the Gd@C(82) and Ce@C(82) junctions. The conductance, on the other hand, remains comparable for all three systems. The power factor determined for the Gd@C(82) based junction is so far the highest obtained for a single-molecule device. Although the encapsulated metal atom does not directly contribute to the transport, we show that the observed enhancement of the thermopower for Gd@C(82) and Ce@C(82) is elucidated by the substantial changes in the electronic- and geometrical structure of the fullerene molecule induced by the encapsulated metal atom.

Length and energy gap dependences of thermoelectricity in nanostructured junctions.

The possibilities of an enhanced thermoelectric figure of merit value, ZT, in a nanostructured junction are examined for a wide range of parameter values in a theoretical model. Our research shows that the figure of merit can take a very large maximum, which depends both on the length and the energy gap values. The maximum of ZT is achieved when the Fermi level of the electrodes is aligned to the edge of the electronic transmission function of the junction, where both the conductance and the Seebeck constant are significantly enhanced. On the basis of our results, we conclude that nanowires and molecular junctions form a special class of systems where a large ZT can be expected in some cases.