Session R37: Focus Session: Nanoscale Conductance Theory I

Conductance Through Single Organometallic Molecules

We have undertaken ab initio calculations of the conductance and I-V curve of a variety of single molecules bridging two metallic leads. The method adopted is a non-equilibrium Green function (NEGF) approach to transport combined with density functional theory (DFT) calculations for the electronic structure.\\ A principal motivation comes from experiments in the U. Maryland group [1]: they showed that a molecule containing a ferrocene moiety conducts nearly perfectly, in striking contrast to the severely impaired conduction through all fully conjugated but non-metallic molecules. Our calculations show that, indeed, there is a transmission resonance at the Fermi energy of the leads connected to the iron atom in the molecule. However, the comparison of theory and experiment also points to significant weaknesses caused by approximations in the standard NEGF+DFT approach.\\ Thus, on a much simpler system -- a H atomic chain -- we carry out much improved calculations involving exact exchange, hybrid functionals, and the optimized effective potential method. These provide a cautionary illustration of the kind and magnitude of errors in the standard approach.\\ Finally, emboldened by our success with the ferrocene-containing molecule, we turn to developing a true molecular spintronics based on cobaltocene moieties (spin 1/2). A simple molecule with a single cobaltocene provides a spin filter; we demonstrate a spintronic switch and spin valve using a dicobaltocene molecule [2].\\\\ (1.) S.A. Getty, et al. (groups of M.S. Fuhrer, and L.R. Sita), PRB 71, 241401(R) (2005).\\ (2.) R.Liu, S.-H. Ke, H.U. Baranger, and W. Yang, Nano Lett. 5, 1959 (2005).\\   

Negative differential resistance (NDR) of ferrocenyl-alkanethiolate on the Au (111) surface

With the rapidly growing interest in the development of molecular electronics, the resonant tunneling diode (RTD) becomes an attractive molecular device goal due to its utility in switching logic and simplicity in integration. Molecular systems displaying Negative Differential Resistance (NDR) and resonant tunneling show great potential as RTDs. In a recent experiment, self-assembled monolayers (SAMs) of ferrocenyl-alkanethiolate on gold show clear molecular NDR, but its mechanism has not been identified. We report first-principles studies of electronic transport in such SAMs by the non-equilibrium Green functions method. The calculated I-V characteristics show strong NDR at both positive and negative biases, which are in good agreement with the experimental results. We find that the ferrocene group acts like a quantum dot and that the resonant coupling between its HOMO and the gold leads is responsible for the NDR features. Such molecules could lead to novel RTDs in nanoscale molecular devices.   

Exploring the lead dependence of single-molecule conductance from first principles: The case of H$_{2}$ molecular junctions

Although the transport properties of several single-molecule junctions have now been reported, only a few studies have systematically examined the sensitivity of the junction conductance to the choice of metallic contacts. Recent break-junction experiments have revealed significantly lower conductance for H$_{2}$ molecular junctions when Pt leads were replaced with Pd,$^{1,2}$ suggesting a dramatic difference in electronic coupling between the molecule and lead. In this work, we examine this coupling directly by computing the conductance of H$_{2}$ with several different metallic contacts using an \textit{ab-initio} scattering state approach$^{3 }$ based on density functional theory.$^{ }$We find that by substituting Pt with Pd leads, the low-bias electron transport crosses over from a ballistic to an off-resonance tunneling regime, leading to a conductance smaller than unity in agreement with experiments. The extent to which substituting different leads may be used to tune the transport properties of this and other simple single-molecule junctions will be discussed. This work was supported by the NSF Grant No. DMR04-39768 and U.S. DOE Contract No. DE-AC03-76SF00098. [1] R. H. M. Smit \textit{et al.}, Nature (London) \textbf{419}, 906 (2002). [2] Sz. Csonka \textit{et al.}, Phys. Rev. Lett. \textbf{93}, 016802 (2004). [3] H.J. Choi, M.L. Cohen and Steven G. Louie, to be published.   

Electronic level alignment at metal-molecule interfaces from first principles

Electronic transport through nanoscale molecular junctions critically depends on the energetic alignment of frontier molecular states with the contact Fermi levels. In this work, a first-principles Green’s function approach is used to explore how frontier molecular energy levels are modified at metal-molecule interfaces. The electronic structure of a model interface, benzene on graphite (0001), is computed using the GW approximation for the electron self-energy operator. Upon adsorption on the surface, the benzene HOMO-LUMO gap is predicted to be 7.2 eV, substantially reduced from its calculated gas-phase value of 10.5 eV, and slightly smaller than its computed solid-phase gap of 7.5 eV. This decrease is attributed to the change in the electronic correlation energy of the frontier states in different environments. Comparison with a classical image interaction provides a quantitative measure of the contribution of the molecule-substrate coupling to the gap narrowing of the molecule.   

Is a molecule a quantum wire or a quantum dot?

We address an important issue regarding the appropriate transport regime for molecular conduction. A typical transport calculation employs the Non Equilibrium Green's function (NEGF) transport scheme coupled with an appropriate self consistent field (SCF) method. This implies that the molecule is treated as a ``quantum wire'', usually applicable when contact couplings are much larger than other energy scales involved. However, there exists a whole class of experimental data whose qualitative features depart significantly from the ones usually explained using the above approach. We show that these features can be naturally addressed by adopting a Coulomb Blockade (CB) approach used in ``quantum dot'' transport. This involves description of the molecule in its many-body space. Our analysis in the many-body space of a prototypical molecule explains the non-trivial features commonly observed in low temperature molecular conduction experiments. Hence, we point out the inadequacy of SCF approaches towards a concrete description of molecular conduction which should involve both quantum chemistry and transport in the many-body space of the molecule.   

Constrained LDA ab-initio calculation of screening of charging energy in C60

Recent measurements and theoretical calculations of the electronic properties of C60 on metal substrates have shown that the electron-electron repulsion parameter U, which determines the coulomb blockade transport properties, is strongly screened in the presence of a metal susbtrate. Since standard Density Functional Theory calculations treat this charging energy in a mean field sense, it ignores the discreteness of the charge on the C60 that is critical to coulomb blockade. To account for the effect of the screened U in transport experiments we calculate the charging energy of C60 in a few environments using a constrained LDA approach and explore the implications for coulomb blockade transport phenomena. This work was supported by National Science Foundation Grant No. DMR04-39768 and by the Director, Office of Science, Office of Basic Energy Sciences, Division of Material Sciences and Engineering, U. S Department of Energy under Contract No. DE-AC03-76SF00098. Computational resources have been provided by DOE at the National Energy Research Scientific Computing Center(NERSC)   

Physical manifestation of the Kohn-Sham energy gap in tunneling currents

Density-functional theory in the Kohn-Sham (KS) approximation yields accurate ground-state properties of molecules and solids. The KS energy gap, however, is much smaller than the gap obtained from experiments that entail electronic excitations. Here we point out that the zero-bias differential resistance of metal-insulator-metal structures is a ground state property and demonstrate that the KS gap, which is a feature of the ground-state KS Hamiltonian, acts as the effective tunnel barrier. The theory is validated by three sets of available data for the resistance of SiO$_2$ films as a function of film thickness.   

Semiconductor/Molecule Transport Junctions: An Analytic Form For The Self-Energies

We have derived an approximate analytic expression for the spectral density of a simple model of a semiconductor/molecule junction. The semiconductor is considered as a tight-binding one-dimensional chain with periodic boundary conditions, and either bond or site-energy, alternation to mimic a two-band system. Using the simplest representation for an atomic or molecular site we obtain a spectral density whose main physical and mathematical features are independent of the alternation pattern. In this contribution, we show applications of our model to the description a variety of junctions where the relative position of the energy levels involved is changed.   

Ab initio study of inleastic transport in molecular electronic devices

One of the most important issues of conduction at nano-scale concerns the effects of atomic vibration. Interaction between electrons and vibrational excitations in nanoelectronic devices has become the problem to solve in order to advance the research field of nanoelectronic theory. Understanding these effects is crucial for predicting device performance. In this talk, we present a method based on Density Functional Theory and Nonequilibrium Green's functions formalism for the calculation of tunneling current and conductance in molecular electronic devices in the presence of electron-phonon interaction. Using self-consistent Born approximation, we can determine the phonon self-energy, the electron Green's function, the electronic density matrix and the electronic Hamiltonian within equal footing of our formalism. As an example, we present numerical results obtained for several molecular electronic devices and show that only few molecular vibrational excitations seem to have an effect on the inelastic tunneling.   

Microscopic Current Flow Patterns in Nanoscale Quantum Point Contacts

Transport in nanoscale conductors has been studied extensively mainly using the stationary scattering approach. However, the dynamical nature of transport, and in particular, the flow patterns of the microscopic current through a nanoscale junction, have remained poorly understood. We apply a novel time-dependent transport approach [1], which combines closed and finite geometries with time-dependent density functional theory,to study current flow patterns in nanoscale quantum point contacts [2]. The results of both atomistic and jellium calculations show that surface charges form dynamically at the junction-electrode interfaces in both abrupt and adiabatic junctions. The curr ent exhibits some characteristics of a classical hydrodynamic liquid but also displays unique patterns arising from the interaction with the surface charges. We also investigate the effect of the flow velocity, charge density, and lattice structures on the electron dynamics. If time permits we also discuss the effects of the viscosity of the electron liquid [3]. Work supported by DOE (DE-FG02-05ER46204). [1] M. Di Ventra and T.N. Todorov, J. Phys. Cond. Matt. 16, 8025 (2004). [2] N. Bushong, N. Sai and, M. Di Ventra, Nano Lett. (in press). [3] N. Sai, M. Zwolak, G. Vignale, and M. Di Ventra, Phys. Rev. Lett. 94, 186810 (2005 ).   

Electron transport in molecular devices

We present an application of a recently proposed quantum-kinetic scheme for non equilibrium transport properties in nanoscale systems, based on a Liouville-master equation for the reduced density operator and combined with a Density Functional Theory description of the electronic structure [1,2]. The systems studied are the well known benzene-dithiol sandwiched between two gold electrodes and the gold quantum point contact. The results we obtain are in general agreement with previous theoretical works and with recent experimental measurements. We analyze the spatial distribution of the current density and the effect of geometrical distortions on the transport properties.