Session U24: Focus Session: Transport in Nanostructures VI: Nonequilibrium Phenomena and Noise

Imaging hot-electron transport using chemical reactions on metal surfaces

We have investigated a new regime of single-molecule excitation in the scanning tunneling microscope, where hot electrons locally injected from the STM tip spread out via surface resonances over length scales of up to 100 nm and electronically excite surrounding molecules causing chemical reactions. Such non-local reactions were observed for several different molecules on the (111), (110) and (100) terminated surfaces of gold and copper. The hot-electron origin of these reactions was differentiated from the possible electric field effect in the tip-surface junction on the basis of the statistical analysis of the dissociation yield as well as the non-local excitation in the presence of artificially fabricated nanoclusters. One of the new opportunities provided by the non-local excitation is a direct measurement of hot-electron transport on a metal surface. Using a phenomenological kinetic model for the statistical analysis of the non-local reactions, it is shown that the reaction rate increases linearly with tunneling current and decays exponentially with the distance from the excitation pulse. Since the attenuation length of the non-local reaction has little dependence on the STM-tip and the parameters of the excitation, we argue that it is proportional to the inelastic mean-free path of hot-electrons in the surface resonance. The angular distribution of the reaction events is isotropic on Au(111), which is consistent with the symmetry of its surface resonances in the energy range of the non-local reaction. It is also shown that the total yield of the non-local reaction provides a measure of hot-electron transport across single-atom steps. Although the reflectance of the hot-electrons by single atom steps on Au(111) is less than 20{\%} at energies above 1.5 V, the yield of the reaction becomes surprisingly asymmetric if hot-electrons are injected in the immediate vicinity of the step.   

Electromigration force, surface resistivity and low-frequency noise

Scattering of charge carriers from surface structures will become an increasing factor in the resistivity as the structure decreases in size to the nanoscale. The measured effects of scattering at the most basic surface defect, a kink in a step edge, are 5x larger than for a freely diffusing surface atom. For thermally active materials, this yields a corresponding contribution of the fluctuating steps to the surface resistivity, which will exceed 1{\%} of the bulk resistivity as wire diameters decrease below 10s of nanometers. The temporal fluctuations of kink density will cause resistivity noise. Relating the known fluctuation spectrum of the step displacements to fluctuations in their lengths, the corresponding resistivity noise is predicted to show spectral signatures of $\sim f^{-1/2}$ for step fluctuations governed by random attachment/ detachment, and $\sim f^{-3/4}$ for step fluctuations governed by step-edge diffusion.   

Frequency-dependent counting statistics in interacting nanoscale conductors

Following the considerable success of shot-noise in the understanding of transport through mesoscopic systems, attention is now turning towards the higher-order statistics of electron current. The so-called Full Counting Statistics (FCS) of electron transport yields all moments (or cumulants) of the probability distribution $P(n,t)$ of the number of transferred electrons during time $t$. The theory of FCS is now well established in the zero-frequency limit. However, this is by no means the full picture, since the higher-order current correlators at finite frequencies contain much more information than their zero-frequency counterparts. In this work [1], we present a formalism to calculate finite-frequency current correlations in interacting nanoscopic conductors. We work within the n-resolved density matrix approach and obtain a multi-time cumulant generating function that provides the fluctuation statistics solely from the spectral decomposition of the Liouvillian. We apply the method to the frequency-dependent third cumulant of the current through a single resonant level and through a double quantum dot. Our results, which show that deviations from Poissonian behaviour strongly depend on frequency, demonstrate the importance of finite-frequency higher-order cumulants in fully characterizing transport. [1] C. Emary, D. Marcos, R. Aguado and T. Brandes, Physical Review B, 76, 161404R, 2007.   

Nonequilibrium elastic quantum transport using plane waves

In this work, we present an \emph{ab initio} nonequilibrium electronic structure method for modeling the elastic electron transport through a nanostructure coupled to semi-infinite external electrodes and with an applied bias voltage. Our method is based on the scheme presented in Ref.\,[1], where the coherent quantum transport is calculated by means of the \emph{exact} scattering states of the system obtained using plane waves and for zero applied bias voltage. In the case of a finite bias voltage, the electronic system is in a nonequilibrium situation, and the problem needs to be solved self-consistently. Here, we present an approach to obtain the self-consistent charge density and potential of the system, which are then employed in the calculation of the nonequilibrium transmission coefficient and conductance. As an illustration, results for a model system made up of a di-thiol-benzene (DBT) molecule connected by two Cu wires are provided. [1] A. Garcia-Lekue and L.W. Wang, Phys. Rev. B. {\bf 74}, 245404 (2006).   

Allowed charge transfers between coherent conductors driven by a time-dependent scatterer

We derive constraints on the statistics of the charge transfer between two conductors in the model of arbitrary time-dependent instant scattering of non-interacting fermions at zero temperature. The constraints are formulated in terms of analytic properties of the generating function: its zeroes must lie on the negative real axis. This result generalizes existing studies for scattering by a time-independent scatterer under time-dependent bias voltage. We discuss the meaning and possible extensions of our results.   

Ab-initio formulation of the 4-point conductance of interacting electronic systems and its implementation in the GWST method

The commonly employed linear-response expression for the conductance of quantum junctions suffers from an ambiguity of the definition of the applied potential difference. We show how this is resolved in terms of the formally as well as physically well defined 4-point conductance [P. Bokes, J. Jung, and R. W. Godby, Phys. Rev. B 76, 125433 (2007)]. Furthermore, expressing the 4 point conductance solely in terms of the density response function or polarizability, we obtain a computationally viable approach to go beyond mean-field, Green's function based descriptions of realistic ab initio models of quantum junctions. We will discuss the numerical implementation of the formalism within the GWST code for the real-space imaginary-time GW method [N. Rojas, R.W. Godby and R.J. Needs, Phys. Rev. Lett. 74 1827 (1995)] and present results for several simple systems.   

Comparison of transport calculations using complex absorbing potentials and the Non-equilibrium Green's function formalism

In the Non-equilibrium Green's formalism (NEGF) the system is divided into left and right leads and a central region. To avoid spurious reflections from the boundaries one has to treat the leads as semi-infinite systems. Various efficient recursion methods are developed [1] for this purpose. Alternatively, one can use a complex absorbing potential (CAP) that absorbs the outgoing waves and one only has to deal with short finite leads. In this work we have compared the NEGF recursion and CAP approaches (1) on a simple analytically solvable example and (2) by calculating the transmission coefficients for a carbon nanotube device using a density functional Hamiltonian. Both approaches give very accurate results but the CAP method is orders of magnitude faster in calculating the self-energies. This work was supported by NSF grant ECS 0622146.   

Systematic Study on Quantum Confinement and Waveguide Effects for Elastic and Inelastic Currents in Atomic Gold Wire: Importance of the Phase Factor for Modeling Electrodes

Quantum confinement of the electrodes is an important issue for electron transport through molecular or atomic wire junctions. To assess the importance of waveguide effects by quantum confinement of the electrodes, we have calculated elastic and inelastic conductance and inelastic electron tunneling spectra of atomic gold wire with gold electrodes for several models. The results show the quite important role of the phase factors between the modeled electrodes and the contact region.   

Nonlinear transport properties of model metal--Mott-insulator--metal heterostructures

Transport properties of heterostructures in which a finite number of correlated-insulator or correlated-metal layers are sandwiched by semi-infinite metallic leads are investigated by using the layer dynamical-mean-field method combined with the Keldysh Green's function technique. We use as impurity solvers the equation-of-motion decoupling method, the noncrossing approximation and the iteration perturbation method. Electron spectral functions in the interacting region are shown to evolve by an applied bias voltage. These effects control the current-voltage characteristics of the heterostructures. It is also shown that the deformed spectral functions strongly affect the optical response. These features differentiate a correlation-induced Mott insulator and a conventional band insulator.   

Phonon Effects on Charge Transport Through a Two State Molecule

We study the effect of local and non-local phonon on the transport properties of a molecule model described by two- electronic states. The local phonon interaction is tackled by means of a Lang–Firsov transformation [1,2]. The interaction with non-local phonons (phonon-assisted hopping) is considered perturbatively up to the first nonzero order in the self energy. The presence of different kinds of electron-phonon interaction open new transmission channels. In addition to the polaron shift and replicas due to local phonons, non-local phonons cause the appearance of new satellite states around the initial states. In the weak coupling regime of non-local phonon and electrons, states are shifted an amount proportional to square of the interaction. However, in the strong coupling regime, the non-linear effects emerge and display more interesting features on transport properties. Additional features on transport properties due to new transmission channel are shown to appear at finite temperatures. [1] G. D. Mahan, Many-particle physics, 3rd ed. (Plenum Publishers, New York, 2000). [2] R. Gutierrez \emph{et al.}, Phys. Rev. B. \textbf{74}, 235105 (2006).