Theoretical considerations -the weak coupling limit……36 5c. Theoretical considerations -moderately strong coupling..41 5d. Comparison of approximation schemes………………….48 5e. Asymmetry in IETS………………………………………51 5f. The origin of dips in IETS signals………………………..53 5g.

Within a simple mean-field model (self-consistent Hartree approximation) we discuss the possibility of polaron formation on a molecular wire as a mechanism for negative differential resistance (NDR), switching, and/or hysteresis in the I-V characteristic of molecular junctions. This mechanism differs from earlier proposed mechanisms of charging and conformational change. The polaron model captures the essential physics and provides qualitative correspondence with experimental data. The importance of active redox centers in the molecule is indicated.

Within a phonon-assisted resonance level model we develop a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. The scheme takes into account the mutual influence of the electron and phonon subsystems. It is based on the 2 nd order cumulant expansion, used to express the correlation function of the phonon shift generator in terms of the phonon momentum Green function. Equation of motion (EOM) method is used to obtain an approximate analog of the Dyson equation for the electron and phonon Green functions in the case of many-particle operators present in the Hamiltonian. To zero-order it is similar in particular cases (empty or filled bridge level) to approaches proposed earlier. The importance of self-consistency in resonance tunneling situations (partially filled bridge level) is stressed. We confirm, even for strong vibronic coupling, a previous suggestion concerning the absence of phonon sidebands in the current vs. gate voltage plot when the source-drain voltage is small 35 .

We study inelastic electron tunneling through a molecular junction using the nonequilibrium Green's function formalism. The effect of the mutual influence between the phonon and the electron subsystems on the electron tunneling process is considered within a general self-consistent scheme. Results of this calculation are compared to those obtained from the simpler Born approximation and the simplest perturbation theory approaches, and some shortcomings of the latter are pointed out. The self-consistent calculation allows also for evaluating other related quantities such as the power loss during electron conduction. Regarding the inelastic spectrum, two types of inelastic contributions are discussed. Features associated with real and virtual energy transfer to phonons are usually observed in the second derivative of the current I with respect to the voltage Phi when plotted against Phi. Signatures of resonant tunneling driven by an intermediate molecular ion appear as peaks in the first derivative dI/dPhi and may show phonon sidebands. The dependence of the observed vibrationally induced lineshapes on the junction characteristics, and the linewidth associated with these features are also discussed.

Much current experimental research on transport in molecular junctions focuses on finite voltages, where substantial polarization-induced nonlinearities may result in technologically relevant device-type responses. Because molecules have strong polarization responses to changing charge state or external field, molecules isolated between electrodes can show strongly nonlinear current-voltage responses. For small applied voltages (up to approximately 0.3 volt), weak interaction between transporting electrons and molecular vibrations provides the basis for inelastic electron tunneling spectroscopy. At higher voltages and for certain time scale regimes, strong coupling effects occur, including Coulomb blockade, negative differential resistance, dynamical switching and switching noise, current hysteresis, heating, and chemical reactions. We discuss a general picture for such phenomena that arise from charging, strong correlation, and polarization (electronic and vibrational) effects in the molecule and at the interface.

Heating and heat conduction in molecular junctions are considered within a general NEGF formalism. We obtain a unified description of heating in current carrying molecular junctions as well as the electron and phonon contributions to the thermal flux, including their mutual influence. Ways to calculate these contributions, their relative importance and ambiguities in their definitions are discussed. A general expression for the phonon thermal flux is derived and used in a new "measuring technique", to define and quantify 'local temperature' in nonequilibrium systems. Superiority of this measuring technique over the usual approach that defines effective temperature using the equilibrium phonon distribution is demonstrated. Simple bridge models are used to illustrate the general approach, with numerical examples.Comment: 31 pages, 12 figure

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit. DOI: 10.1103/PhysRevLett.114.080602 PACS numbers: 05.70.Ln, 05.60.Gg Nonequilibrium thermodynamics of open quantum systems is a powerful tool for the study of mesoscopic and nanoscale systems. It allows one to reliably assess the performance of energy-converting devices such as thermoelectrics or photoelectrics, by identifying the system entropy production. It enables one to meaningfully compare these different devices by discriminating the systemspecific features from the universal ones and to appraise the role of quantum effects. It can also be used to verify the thermodynamic consistency of approximation schemes. Such a theory is nowadays available for systems weakly interacting with their surrounding [1][2][3][4][5][6], where it has proven very useful [7][8][9][10][11][12][13][14][15]. However, in case of strong system-reservoir interactions, finding definitions for heat, work, entropy, and entropy production, which satisfy the basic laws of thermodynamics is an open problem. Each proposal has its own limitations [16][17][18][19][20][21][22][23], even at equilibrium [24][25][26][27][28][29][30]. Reversible transformations, for instance, are never explicitly characterized. Establishing a consistent nonequilibrium thermodynamics for open quantum systems strongly coupled to their surrounding is therefore an important step towards a more realistic thermodynamic description of mesoscopic and nanoscale devices. It is also essential to improve our understanding of the microscopic foundations of thermodynamics.In this Letter, we use the nonequilibrium Green's functions (NEGF) to establish a fully consistent nonequilibrium thermodynamic description of a fermionic single quantum level strongly coupled to multiple fermionic reservoirs. A slow time-dependent driving force controls the level energy as well as the system-reservoir interaction. We propose definitions for the particle number, the energy, and the entropy of the system, as well as for entropy production, heat, and work, which give rise to a consistent zeroth, first, second, and third law. These definitions can be seen as energy resolved versions of the weak coupling definitions used in stochastic thermodynamics. An interesting outcome of our approach is that the general form of the energy and particle currents is different from the standard form used in the NEGF and cannot be expressed as an expectation value of operators. We recover the known expressions when considering nonequilibrium steady states (i.e., in absenc...

The interaction of light with molecular conduction junctions is attracting growing interest as a challenging experimental and theoretical problem on one hand, and because of its potential application as a characterization and control tool on the other. It stands at the interface between two important fields, molecular electronics and molecular plasmonics and has attracted attention as a challenging scientific problem with potentially important technological consequences. Here we review the present state of the art of this field, focusing on several key phenomena and applications: using light as a switching device, using light to control junction transport in the adiabatic and non-adiabatic regimes, light generation in biased junctions and Raman scattering from such systems. This field has seen remarkable progress in the past decade, and the growing availability of scanning tip configurations that can combine optical and electrical probes suggests that further progress towards the goal of realizing molecular optoelectronics on the nanoscale is imminent.