A polaron model proposed as a possible mechanism for nonlinear conductance [Galperin M, Ratner M A, and Nitzan A 2005 Nano Lett. 5 125-30] is revisited with focus on the differences between the weak and strong molecule-lead coupling cases. Within the one-molecular level model we present an approximate expression for the electronic Green function corresponding to inelastic transport case, which in the appropriate limits reduces to expressions presented previously for the isolated molecule and for molecular junction coupled to a slow vibration (static limit). The relevance of considerations based on the isolated molecule limit to understanding properties of molecular junctions is discussed.
The charge-memory effect, bistability and switching between charged and neutral states of a molecular junction, as observed in recent STM experiments, is considered within a minimal polaron model. We show that in the case of strong electron-vibron interaction the rate of spontaneous quantum switching between charged and neutral states is exponentially suppressed at zero bias voltage but can be tuned through a wide range of finite switching timescales upon changing the bias. We further find that, while junctions with symmetric voltage drop give rise to random switching at finite bias, asymmetri…
We investigate the full-counting statistics (FCS) of energy transport carried by electrons in molecular junctions for the Anderson-Holstein model in the polaronic regime. Using two-time quantum measurement scheme, generating function (GF) for the energy transport is derived and expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. Dressed tunneling approximation is used in decoupling the phonon cloud operator in the polaronic regime. This formalism enables us to analyze the time evolution of energy transport dynamics after a sudden switch-o…
The Holstein Hamiltonian was proposed half a century ago; since then, decades of research have come up empty handed in the pursuit of a closed-form solution. An exact solution to the two-site Holstein model is presented in this paper. The obtained results provide a clear image of the Hamiltonian structure and allow for the investigation of the symmetry, energy level crossings and polaronic characteristics of the system. The main mathematical tool is a three-term recurrence relation between the wave function amplitudes that was obtained using the properties of a family of orthogonal functions, …
We study the interplay of polaronic effect and superconductivity in transport through molecular Josephson junctions. The tunneling rates of electrons are dominated by vibronic replicas of the superconducting gap, which show up as prominent features in the differential conductance for the dc and ac current. For relatively large molecule-lead coupling, a features that appears when the Josephson frequency matches the vibron frequency can be identified with an over-the-gap structure observed by Marchenkov et al. [Nat. Nanotech. 2, 481 (2007)]. However, we are more concerned with the weak-coupling …
We investigate the influence of vibrational phonon modes on the entanglement through a quantum dot molecule under the bias voltage-driven field. The molecular quantum dot system can be realized by coupled quantum dots in the middle of the suspended carbon nanotube. This system would be described by the Anderson-Holstein model and also can be analyzed by the polaron master equation in Markovian regime. In the presence of electron-phonon interaction, we study the entanglement as a function of bias voltage and temperature. Despite entanglement degradation because of phonon decoherence, we employ …
Nanoscale magnetic tunnel junction plays a pivotal role in magnetoresistive random access memories. Successful implementation depends on a simultaneous achievement of low switching current for the magnetization switching by spin-transfer torque and high thermal stability, along with a continuous reduction of junction size. Perpendicular-easy-axis CoFeB/MgO stacks possessing interfacial anisotropy have paved the way down to 20-nm scale, below which a new approach needs to be explored. Here we show magnetic tunnel junctions that satisfy the requirements at ultrafine scale by revisiting shape ani…
Negative differential resistance (NDR) is tuned at junctions of electronically different dimer and trimer of Rose Bengal on an atomic flat gold (111) surface. Isolated molecule did not show any NDR. But it was induced to show double NDR with large peak to valley ratio (1.8~3.1) in room temperature via charging its neighbor reproducibly by an electrical pulse. In some sections of junction by applying pulse one could destroy the phenomenon or regenerate it by STM manipulation of molecules. NDR was also independent of polaronic nature. It was possible to write bits 1 and 0 for cationic NDR (in di…
We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical res…
The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4π$ (rather than a $2π$) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short- and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and f…
The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat many-body quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show t…
The energy dissipation and heat flows associated with the particle current in a system with a molecular junction are considered. In this connection, we determine the effective temperature of the molecular oscillator that is compatible with the existence of a steady state. The calculations based on the Kadanov-Baym nonequilibrium Green function formalism are carried out supposing a strong coupling of the dot electrons with the molecular vibrations. Accordingly, the representation given by the Lang-Firsov polaron transformation is used and the dependence of results on the electron-phonon interac…
Here we present a theoretical analysis of inelastic effects on thermoelectric properties of molecular-scale junction in both linear and nonlinear response regimes. Considered device is composed of molecular quantum dot (with discrete energy levels) asymmetrically connected to metallic electrodes (treated within the wide-band approximation) via potential barriers, where molecular vibrations are modeled as dispersionless phonon excitations. Nonperturbative computational scheme, used in this work, is based on Green's function theory within the framework of polaron transformation (GFT-PT) which ma…
By using a propagation scheme for current matrices and an auxiliary mode expansion method, we investigate the transient dynamics of a single molecular junction coupled with a vibrational mode. Our approach is based on the Anderson-Holstein model and the dressed tunneling approximation for the electronic self-energy in the polaronic regime. The time-dependent currents after a sudden switching on the tunneling to leads and an abrupt upward step bias pulse are calculated. We show that the strong electron-phonon interaction greatly influences the nonlinear response properties of the system, and gi…
We present a theoretical approach to solve Markovian master equation for quantum transport with stochastic telegraph noise. Considering probabilities as functionals of a random telegraph process we use the Novikov's functional method to convert stochastic master equation to a set of deterministic differential equations. The equations are then solved in the Laplace space and the expression for the probability vector averaged over ensemble of realisations of stochastic process is obtained. We apply the theory to study manifestations of telegraph noise in transport properties of molecular junctio…
The interaction between electronic and vibrational degrees of freedom is an important mechanism in nonequilibrium charge transport through molecular nanojunctions. While adiabatic polaron-type coupling has been studied in great detail, new transport phenomena arise for nonadiabatic coupling scenarios corresponding to a breakdown of the Born-Oppenheimer approximation. Employing the numerically exact hierarchical equations of motion approach, we analyze the effect of nonadiabatic electronic-vibrational coupling on electron transport in molecular junctions considering a series of models with incr…
Currently, molecular tunnel junctions are recognized as important active elements of various nanodevices. This gives a strong motivation to study physical mechanisms controlling electron transport through molecules. Electron motion through a molecular bridge is always somewhat affected by the environment, and the interactions with the invironment could change the energy of the traveling electron. Under certain conditions these inelastic effects may significantly modify electron transport characteristics. In the present work we describe inelastic and dissipative effects in the electron transpor…
We use the recently proposed scattering states numerical renormalization group (SNRG) approach to calculate $I(V)$ and the differential conductance through a single molecular level coupled to a local molecular phonon. We also discuss the equilibrium physics of the model and demonstrate that the low-energy Hamiltonian is given by an effective interacting resonant level model. From the NRG level flow, we directly extract the effective charge transfer scale $Γ_{\rm eff}$ and the dynamically induced capacitive coupling $U_{\rm eff}$ between the molecular level and the lead electrons which turns ou…
We consider the steady-state thermoelectric transport through a vibrating molecular quantum dot that is contacted to macroscopic leads. For moderate electron-phonon interaction strength and comparable electronic and phononic timescales, we investigate the impact of the formation of a local polaron on the thermoelectric properties of the junction. We apply a variational Lang-Firsov transformation and solve the equations of motion in the Kadanoff-Baym formalism up to second order in the dot-lead coupling parameter. We calculate the thermoelectric current and voltage for finite temperature differ…
The calculation of the nonlinear conductance of a single-molecule junction is revisited. The self energy on the junction resulting from the electron-phonon interaction has at low temperatures logarithmic singularities (in the real part) and discontinuities (in the imaginary one) at the frequencies corresponding to the opening of the inelastic channels. These singularities generate discontinuities and logarithmic divergences (as a function of the bias voltage) in the low-temperature differential conductance around the inelastic thresholds. The self energy also depends on the population of the v…
We study the photo-assisted noise generated by time-dependent or random sources and transmission amplitudes. We show that it obeys a perturbative non-equilibrium fluctuation relation that fully extends the lateral-band transmission picture in terms of many-body correlated states. This relation holds in non-equilibrium strongly correlated systems such as the integer or fractional quantum Hall regime as well as in quantum circuits formed by a normal or Josephson junctions strongly coupled to an electromagnetic environment, with a possible temperature bias. We then show that the photo-assisted no…
It was observed in recent experiments that the current-voltage characteristics (IV) of BPDN-DT (bipyridyl- dinitro- oligophenylene- ethynylene- dithiol) can be switched in a very controlled manner between "on" and "off" traces by applying a pulse in a bias voltage, V_bias. We have calculated the polaron formation energies to check a frequently held belief, namely, that the polaron formation can explain the observed bistability. Our results are not consistent with such a mechanism. Instead, we propose a conformational reorientation. The molecule carries an intrinsic dipole moment which couples …
Electronic transport properties for single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions or by means of scanning tunneling microscopes. In parallel, many theoretical tools have been developed and refined for describing such transport properties and for obtaining numerical predictions. Most prominent among these theoretical tools are those based upon density functional theory. In this review, theory and experiment are critically compared and this confrontation leads to several important c…
We theoretically investigate the transport properties of a molecule embedded in one arm of a mesoscopic Aharonov-Bohm interferometer. Due to the presence of phonons the molecule level position ($ε_d$) and the electron-electron interaction ($U$) undergo a \emph{polaronic shift} which affects dramatically the electronic transport through the molecular junction. When the electron-phonon interaction is weak the linear conductance presents Fano-line shapes as long as the direct channel between the electrodes is opened. The observed Fano resonances in the linear conductance are originated from the i…
