Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport.

Molecule-electrode interfaces in molecular electronic junctions are prone to chemical reactions, structural changes, and localized heating effects caused by electric current. These can be exploited for device functionality or may be degrading processes that limit performance and device lifetime. We develop a nonequilibrium Green's function based transport theory in which the central region atoms and, more importantly, atoms on molecule-electrode interfaces are allowed to move. The separation of time-scales of slow nuclear motion and fast electronic dynamics enables the algebraic solution of the Kadanoff-Baym equations in the Wigner space. As a result, analytical expressions for dynamical corrections to the adiabatically computed Green's functions are produced. These dynamical corrections depend not only on the instantaneous molecular geometry but also on the nuclear velocities. To make the theoretical approach fully self-consistent, the same time-separation approach is used to develop expressions for the adiabatic, dissipative, and stochastic components of current-induced forces in terms of adiabatic Green's functions. Using these current induced forces, the equation of motion for the nuclear degrees of freedom is cast in the form of a Langevin equation. The theory is applied to model molecular electronic junctions. We observe that the interplay between the value of the spring constant for the molecule-electrode chemical bond and electronic coupling strength to the corresponding electrode is critical for the appearance of structural instabilities and, consequently, telegraphic switching in the electric current. The range of model parameters is identified to observe structurally stable molecular junctions as well as various different kinds of current-induced telegraphic switching. The interfacial structural instabilities are also quantified based on current noise calculations.

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.

Ab initio electron propagator methods are developed to study electronic properties of molecular systems with strong electron-electron and electron-phonon interactions. For the calculation of electron Green's functions we apply a canonical small polaron transformation that intrinsically contains strong electron-phonon effects. In the transformed Hamiltonian, the energy levels for the noninteracting particles are shifted down by the relaxation (solvation) energies. The Coulomb integrals are also renormalized by the electron-phonon interaction. For certain values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative which implies the attraction between two electrons. Within the small polaron transformation we develop a diagrammatic technique for the calculation of electron Green's function in which the electron-phonon interaction is already included into the multiple phonon correlation functions. Since the decoupling of the phonon correlation functions is impossible, and therefore, a Wick's theorem for such correlation functions is invalid, there is no Dyson equation for the electron Green's function. To find the electron Green's function, we use different approximations. One of them is a link-cluster approximation that includes diagonal transitions for the renormalized zeroth Green's function. In the linked-cluster approach the Dyson equation is derived in the most general case, where the self-energy operator is an arbitrary functional (not only in the Hartree-Fock approximation). It is shown that even a Hartree-Fock electron (hole) is not a particle any longer. It is a quasiparticle with a finite lifetime that depends on energy of particle and hole states in different ways. As a consequence of this, a standard description of a Hartree-Fock approximation in terms of wave functions becomes inappropriate in this problem. To challenge the linked-cluster approximation we develop a different approach: a sequential propagation approximation where scattering events occur only for sequential transitions. A self-consistent Hartree-Fock equation for a four-index Green's function matrix is derived. In conclusion, the proposed schemes can be considered for future method developments for quantum chemical calculations for large molecules with strong nonadiabatic effects, e-e correlated electron transfer reactions, and electron transport in molecular transport junctions.

The molecular junction geometry is modeled in terms of nuclear degrees of freedom that are embedded in a stochastic quantum environment of non-equilibrium electrons. The time-evolution of the molecular geometry is governed via a mean force, a frictional force, and a stochastic force, forces arising from many electrons tunneling across the junction for a given nuclear vibration. Conversely, the current-driven nuclear dynamics feed back to the electronic current, which can be captured according to the extended expressions for the current that have explicit dependences on classical nuclear velocities and accelerations. Current-induced nuclear forces and the non-adiabatic electric current are computed using non-equilibrium Green's functions via a timescale separation solution of Keldysh-Kadanoff-Baym equations in the Wigner space. Applying the theory to molecular junctions demonstrated that non-adiabatic corrections play an important role when nuclear motion is considered non-equilibrium and, in particular, showed that non-equilibrium and equilibrium descriptions of nuclear motion produce significantly different current characteristics. It is observed that non-equilibrium descriptions generally produce heightened conductance profiles relative to the equilibrium descriptions and provide evidence that the effective temperature is an effective measure of the steady-state characteristics. Finally, we observe that the non-equilibrium descriptions of nuclear motion can give rise to the Landauer blowtorch effect via the emergence of multi-minima potential energy surfaces in conjunction with non-uniform temperature profiles. The Landauer blowtorch effect and its impact on the current characteristics, waiting times, and the Fano factor are explored for an effective adiabatic potential that morphs between a single, double, and triple potential as a function of voltage.

The effect of inelastic scattering on quantum electron transport through double-barrier resonant-tunneling structures with large cross-sectional areas is studied numerically using the approach based on the nonequilibrium Green's-function formalism of Keldysh, Kadanoff, and Baym. The Markov assumption is not made, and the energy coordinate is retained. This makes the inclusion of the phonon-energy spectrum straightforward both conceptually and in practice. The electron-phonon interaction is treated in the self-consistent first Born approximation (SCFBA). The Pauli exclusion principle is taken into account exactly within the SCFBA. The retention of the energy coordinate allows the calculation of a number of quantities that give insight into the effect of inelastic scattering on electron transport: The effect of inelastic scattering on the occupation of the energy levels, the density of states, the energy distribution of the current density, and the power density is calculated from a quantum kinetic equation for actual device structures under high bias.

The electronic structure of organic-inorganic interfaces often features resonances originating from discrete molecular orbitals coupled to continuum lead states. An example is molecular junction, individual molecules bridging electrodes, where the shape and peak energy of such resonances dictate junction conductance, thermopower, I-V characteristics, and related transport properties. In molecular junctions where off-resonance coherent tunneling dominates transport, resonance peaks in the transmission function are often assumed to be Lorentzian functions with an energy-independent broadening parameter Γ. Here we define a new energy-dependent resonance broadening function, Γ(E), based on diagonalization of non-Hermitian matrices, which can describe resonances of a more complex, non-Lorentzian nature and can be decomposed into components associated with the left and right leads, respectively. We compute this quantity via an ab initio non-equilibrium Green's function (NEGF) approach based on density functional theory (DFT) for both symmetric and asymmetric molecular junctions, and show that our definition of Γ(E), when combined with Breit-Wigner formula, reproduces the transmission calculated from DFT-NEGF. Through a series of examples, we illustrate how this approach can shed new light on experiments and understanding of junction transport properties in terms of molecular orbitals.

We report the implementation of the fully relativistic exact muffin-tin orbital (EMTO) method for both first-principles electronic structure and quantum transport simulation of magnetic and nonmagnetic device materials. We consider a device-material system containing the inevitable atomic disorders in contact with different electrode materials. The Kohn-Sham Dirac equations for both cases with and without spin polarization are self-consistently solved for the central device-material system with the Green's function method. The fully relativistic charge-current density, conventional Pauli spin current density, and transmission coefficient are formulated with the nonequilibrium Green's function technique. To treat the influence of disordered defects/impurities, we combine the nonequilibrium Green's function in the Keldysh space with the coherent potential approximation, and account for the multiple disorder scattering by vertex corrections to a two-Green's-function correlator to calculate the disorder-averaged charge and spin current density. As a demonstration of the present implementation, we calculate the electronic structure of the bulk Pt, Co, and HgTe and Rashba-type surface states of Au and $\mathrm{Ag}/{\mathrm{Ag}}_{2}{\mathrm{Bi}}_{1}$ alloy surfaces. We find that the EMTO electronic structures of all the calculated systems agree well with the results of the projector-augmented wave method. The electronic charge and spin transport implementations are tested with perfect and disordered Cu/Co/Pt/Cu junctions. The important effects of interface and atomic disorders are illustrated for the spin transport in the presence of relativistic effects. The implementation of the fully relativistic EMTO-based device-material simulation provides an important tool for analyzing both the charge and spin transport through nanostructures and materials, significantly extending the capability of first-principles material design for spintronic device applications.

A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nano devices, molecular junctions or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state $\hat{\rho}^S$, constructed as the steady-state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both, the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark the new scheme on two experimentally relevant systems in the single-electron transistor regime: An electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of the new method improve significantly with respect to the plain quantum maste equation treatment at modest additional computational cost.

The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. Corrections for the electronic self-energy are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. The equations for the Bose-like Green's functions have been derived, describing the collective modes: the magnons and doublons. The properties of the poles of the doublon Green's functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green's function has a soft mode at the wave vector Q=(pi,pi,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering.

We present a theory of molecular motors based on the Ehrenfest dynamics for nuclear coordinates and the adiabatic limit of the Kadanoff-Baym equations for current-induced forces. Electron-electron interactions can be systematically included through many-body perturbation theory, making the nonequilibrium Green's function formulation suitable for first-principles treatments of realistic junctions. The method is benchmarked against simulations via real-time Kadanoff-Baym equations, finding an excellent agreement. Results on a paradigmatic model of a molecular motor show that correlations can change dramatically the physical scenario by, e.g., introducing a sizable damping in self-sustained van der Pol oscillations.

Confined nanoscale spaces, electric fields, and tunneling currents make the molecular electronic junction an experimental device for the discovery of new out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining the Keldysh nonequilibrium Green's function treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers first-passage time calculations. The nonequilibrium Green's functions (NEGF) provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving in an external potential in an inhomogeneous medium with a position-dependent friction and diffusion coefficient, is used to obtain an analytic expression for the first-passage time. The theory is applied to several transport scenarios: a molecular junction with a single reaction coordinate dependent molecular orbital and a model diatomic molecular junction. We demonstrate the natural emergence of Landauer's blowtorch effect as a result of the interplay between the configuration dependent viscosity and diffusion coefficients. The resultant localized heating in conjunction with the bond-deformation due to current-induced forces is shown to be the determining factors when considering chemical reaction rates, each of which results from highly tunable parameters within the system.

A numerical method for calculation electronic structure of a nanosystem\ncomposed of a pseudoisocyanine (PIC) molecule assembled on a silver\nnanoparticle is developed. The electronic structure of the silver nanoparticle\ncontaining 125 atoms is calculated within the local density version of the\ndensity functional method. A model of an Ag atom embedded in the center of a\nspherical jellium cluster is used. The host electron Green function is\ncalculated by means of the spherically symmetric expansion. The principal\ntheoretical tool is the scattering theory using the Green function method. The\nmolecule -- silver nanoparticle interaction is studied using the approach\nsimilar to that of the Anderson model for transition metal impurities in\nsolids. Localized levels are shown to split off from the top of the band of the\nnanosystem. The electronic structure calculations yield information on the\ncharacter of chemical bonding in the PIC molecule --- silver particle\nnanosystem.\n

We discuss within the nonequilibrium Green's function formalism the self-consistent Born approximation of the electronic self-energy for concurrent coupling of charge carriers to photons and phonons. The expansion of the charge carrier Green's function is shown to provide a description for a range of physical processes with relevance for the photovoltaic device operation, such as indirect optical transitions, thermally assisted photocarrier escape from quantum wells or phonon-mediated interband transfer in tunnel junctions. The nonequilibrium Green's function picture of these processes is reviewed with focus on the evolution of the system towards the steady state in the convergence of the self-consistency iteration process and on the impact of inelastic scattering on device operation.

Significant effects of magnetic electrodes on rhenium phthalocyanine molecules

Density functional theory (DFT) combined with nonequilibrium Green's function (NEGF) formalism are used to investigate the effects of substitutional doping by nitrogen and sulfur on transport properties of AGNR-pentalene-AGNR nanojunction. A considerable spin filtering capability in a wide bias range is observed for all systems, which may have potential application in spintronics devices. Moreover, all model devices exhibit a negative differential effect with considerable peak-to-valley ratio. Thus, our findings provide a way to produce multifunctional spintronic devices based on nitrogen and sulfur doped pentalene-AGNR nanojunctions. The underlying mechanism for this interesting behavior was exposed by analyzing the transmission spectrum as well as the electrostatic potential distribution. In addition, a system doped with an odd number of dopant shows a rectifying efficiency comparable to other systems. The above findings strongly imply that such a multifunctional molecular device would be a useful candidate for molecular electronics. Graphical abstract The graphene-pentalene-graphene molecular junction.