Wide-band Limit Approximation Research Articles

Spin splitter and spin filter in a three terminals device under Zeeman effect in a tight binding approach

In this work we propose a theoretical study of impurities effects in charge transport through a linear and an aromatic three terminals device under an external magnetic field. We use the Landauer approach, with the electronic structure treated at tight binding (TB) level and model the self-energy with the wide band limit approximation. For the linear chain, we use decimation techniques to renormalize the system, reducing it into a 3 × 3 matrix, so as to make an analytical treatment. For aromatic systems we opt for numerical calculations. Our main results suggest that no matter the system, by introducing impurities into the chain together with an applied magnetic field, there is a possibility to have filter spin (through the system) or splitter spins (on each branch), due to the Zeeman effect. The results agree with other theoretical works for systems with also intrinsic asymmetry of the device but caused by the different polarization into distinct branches. Also, our theoretical approach reveals, in a clear way, how the impurity on each branch makes the system behaves like a spin filter or a spin splitter, depending on the onsite energies of the impurities.

Interacting Electrons in a Flat‐Band System within the Generalized Kadanoff–Baym Ansatz

In this work, the study of the spectral properties of an open interacting system by solving the generalized Kadanoff‐Baym ansatz (GKBA) master equation for the single‐particle density matrix, namely the time‐diagonal lesser Green's function, is reported. To benchmark its validity, the solution obtained within the GKBA is compared with the solution of the Dyson equation at stationarity. In both approaches, the interaction is treated within the self‐consistent second‐order Born approximation, whereas the GKBA still retains the retarded propagator calculated at the Hartree–Fock (HF) and wideband limit approximation level. The model chosen is that of two leads connected through a central correlated region where particles can interact and utilize the stationary particle current at the boundary of the junction as a probe of the spectral features of the system. The central region is chosen as the simplest model featuring a degenerate ground state with a flat band. The main result is that the solution of the GKBA master equation captures well the spectral feature of such system and specifically the transition from dispersionless to dispersive behavior of the flat band as the interaction is increased. Therefore, the GBKA solution retains the main spectral features of the self‐energy used even when the propagator is at the HF level.

Thermoelectric study of the time-dependent resonant level model

We study the non-interacting time-dependent resonant level model mimicking a driven quantum dot connected through leads to two electronic reservoirs held at different temperatures and electrochemical potentials. Using a scattering approach, we provide analytical formulas of the time-dependent particle currents, heat currents, and input driving power under the wideband limit approximation. We also derive Landauer formulas for the corresponding time-integrated quantities when the perturbation applied on the dot is of finite duration. Then, we focus on the case of a single square pulse, benchmark our analytical results against numerical ones that are valid beyond the wideband limit, and perform numerical simulations for a smooth square pulse and a periodic square pulse train. Finally, we discuss whether the efficiency of the device in a stationary Seebeck configuration can be enhanced by driving the dot potential. We find numerically that the transient increase of the efficiency observed in some cases is eventually canceled out at long times.

A Green's Function Approach for Determining Surface Induced Broadening and Shifting of Molecular Energy Levels.

Upon adsorption of a molecule onto a surface, the molecular energy levels (MELs) broaden and change their alignment. This phenomenon directly affects electron transfer across the interface and is, therefore, a fundamental observable that influences electrochemical device performance. Here, we propose a rigorous parameter-free framework, built upon the theoretical construct of Green's functions, for studying the interface between a molecule and a bulk surface and its effect on MELs. The method extends beyond the usual wide-band limit approximation, and its generality allows its use with any level of electronic structure theory. We demonstrate its ability to predict the broadening and shifting of MELs as a function of intramolecular coupling, molecule/surface coupling, and the surface density of states for a molecule with two MELs adsorbed on a one-dimensional model metal surface. The new approach could help provide guidelines for the design and experimental characterization of electrochemical devices with optimal electron transport.

Transport through a biphenyl system as a function of torsion angle: An effective coupling model approach

We present a non-self-consistent renormalized model to calculate the electron transmission through a single molecule connected to two metallic terminals. The treatment is an improvement of a decimation technique, once all relevant parameters of the model were extracted from ab initio calculations performed for an extended system comprising the molecule sandwiched by two metallic clusters. Moreover, calculations were done for different values of the applied electric field so as to take account changes in the electronic structure due to this field. We applied this approach to describe the electron transport through a system composed of two phenyl rings connected at different torsion angles, with the self-energy modeled at the wideband limit approximation. The proposed model captures the main features of the molecular system and provides a simple interpretation of the charge transport characteristics, and overall, the results are in a general good agreement with the theoretical and experimental data available in the literature.

Electronic transport through odd-even methylenic spacers connected to an aromatic ring

In this work we propose a theoretical study of charge transport through a nanostructure composed by a methylenic bridge with a phenyl ring at the end, attached between a small silicon cluster in the bottom and a small lead cluster at the top. We use the Non Equilibrium Green Function theory (NEGF-theory) approach, with the electronic structure treated at the density functional theory (DFT) level and model the self energy with the wide band limit approximation. By varying the size of the methylenic bridge from two to five carbons, we show that a geometrical odd–even effect appears in charge transport for cryogenic temperatures, while it is suppressed at room temperature. Such phenomenon was studied by combining MD simulations with ab-initio NEGF transport calculations, thus accounting for the thermal effects. Our theoretical approach reveals the role of avoided-crossing effect on system conductance, occurring only for some alkyl bridge lengths.

Excitation transport in quasi-one-dimensional quantum devices: a multiscale approach with analytical time-dependent non-equilibrium Green’s function

Under the wide-band limit approximation for electrodes, this research proposes analytical time-dependent non-equilibrium Green’s function (TD-NEGF) formulae to investigate dynamical functionalities of quasi-one-dimensional quantum devices, especially for (microwave) photon-assisted transports. Together with a multiscale approach by lumped element model, we also study the effects of transiently-transferring charges to reflect the non-conservation of charges in open quantum systems, and implement numerical calculations in hetero-junction systems composed of functional quantum devices and electrode-contacts (to the environment). The results show that (i) the current calculation by the analytical algorithms, versus those by conventional numerical integrals, presents superior numerical stability on a large-time scale, (ii) the correction of charge transfer effects can better clarify non-physical transport issues, e.g. the blocking of AC signaling under the assumption of conventional constant hamiltonian, (iii) the current in the long-time limit validly converges to the steady value obtained by standard time-independent density functional calculations, and (iv) the occurrence of the photon-assisted transport is well-identified.

Charge separation and dissipation in molecular wires under a light radiation

Photo-induced charge separation in nanowires or molecular wires had been studied in previous experiments and simulations. Most researches deal with the carrier diffusions with the classical phenomenological models, or the static energy levels by quantum mechanics calculations. Here we give a dynamic quantum investigation on the charge separation and dissipation in molecule wires. The method is based on the time-dependent non-equilibrium Green's function theory. Polyacetylene chain and poly-phenylene are used as model systems with a tight-binding Hamiltonian and the wide band limit approximation in this study. A light pulse with the energy larger than the band gap is radiated on the system. The evolution and dissipation of the non-equilibrium carriers in the open nano systems are studied. With an external electric potentials or impurity atoms, the charge separation is observed. Our calculations show that the separation behaviors of the electron/hole wave packets are related to the Coulomb interaction, light intensity and the effective masses of electron/hole in the molecular wire.

Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias

Working within the Nonequilibrium Green's Function (NEGF) formalism, a formula for the two-time current correlation function is derived for the case of transport through a nanojunction in response to an arbitrary time-dependent bias. The one-particle Hamiltonian and the Wide Band Limit Approximation (WBLA) are assumed, enabling us to extract all necessary Green's functions and self energies for the system, extending the analytic work presented previously [Ridley et al. Phys. Rev. B (2015)]. We show that our new expression for the two-time correlation function generalises the B\"uttiker theory of shot and thermal noise on the current through a nanojunction to the time-dependent bias case including the transient regime following the switch-on. Transient terms in the correlation function arise from an initial state that does not assume (as is usually done) that the system is initially uncoupled, i.e. our approach is partition-free. We show that when the bias loses its time-dependence, the long time-limit of the current correlation function depends on the time difference only, as in this case an ideal steady state is reached. This enables derivation of known results for the single frequency power spectrum and for the zero frequency limit of this power spectrum. In addition, we present a technique which for the first time facilitates fast calculations of the transient quantum noise, valid for arbitrary temperature, time and voltage scales. We apply this to the quantum dot and molecular wire systems for both DC and AC biases, and find a novel signature of the traversal time for electrons crossing the wire in the time-dependent cross-lead current correlations.

Fluctuating-bias controlled electron transport in molecular junctions

We consider the problem of transport through a multiterminal molecular junction in the presence of a stochastic bias, which can also be used to describe transport through fluctuating molecular energy levels. To describe these effects, we first make a simple extension of our previous work [Phys. Rev. B 91, 125433 (2015)] to show that the problem of tunneling through noisy energy levels can be mapped onto the problem of a noisy driving bias, which appears in the Kadanoff-Baym equations for this system in an analogous manner to the driving term in the Langevin equation for a classical circuit. This formalism uses the nonequilibrium Green's function method to obtain analytically closed formulas for transport quantities within the wide-band limit approximation for an arbitrary time-dependent bias and it is automatically partition free. We obtain exact closed formulas for both the colored and white noise-averaged current at all times. In the long-time limit, these formulas possess a Landauer-B\uttiker--type structure which enables the extraction of an effective transmission coefficient for the transport. Expanding the Fermi function into a series of simple poles, we find an exact formal relation between the parameters which characterize the bias fluctuations and the poles of the Fermi function. This enables us to describe the effect of the temperature and the strength of the fluctuations on the averaged current which we interpret as a quantum analog to the classical fluctuation-dissipation theorem. We use these results to convincingly refute some recent results on the multistability of the current through a fluctuating level, simultaneously verifying that our formalism satisfies some well-known theorems on the asymptotic current. Finally, we present numerical results for the current through a molecular chain which demonstrate a transition from nonlinear to linear $I\text{\ensuremath{-}}V$ characteristics as the strength of fluctuations is increased, as well as a stochastic resonance effect in the conductance of this system.

Calculation of the current response in a nanojunction for an arbitrary time-dependent bias: application to the molecular wire

Recently [Phys. Rev. B 91, 125433 (2015)] we derived a general formula for the time-dependent quantum electron current through a molecular junction subject to an arbitrary time-dependent bias within the Wide Band Limit Approximation (WBLA) and assuming a single particle Hamiltonian. Here we present an efficient numerical scheme for calculating the current and particle number. Using the Padé expansion of the Fermi function, it is shown that all frequency integrals occurring in the general formula for the current can be removed analytically. When the bias in the reservoirs is assumed to be sinusoidal it is possible to manipulate the general formula into a form containing only summations over special functions. To illustrate the method, we consider electron transport through a one-dimensional molecular wire coupled to two leads subject to out-of-phase biases. We also investigate finite size effects in the current response and particle number that result from the switch-on of this bias.

Time-dependent density functional theory quantum transport simulation in non-orthogonal basis

Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed.

Dissipative time-dependent quantum transport theory

A dissipative time-dependent quantum transport theory is developed to treat the transient current through molecular or nanoscopic devices in presence of electron-phonon interaction. The dissipation via phonon is taken into account by introducing a self-energy for the electron-phonon coupling in addition to the self-energy caused by the electrodes. Based on this, a numerical method is proposed. For practical implementation, the lowest order expansion is employed for the weak electron-phonon coupling case and the wide-band limit approximation is adopted for device and electrodes coupling. The corresponding hierarchical equation of motion is derived, which leads to an efficient and accurate time-dependent treatment of inelastic effect on transport for the weak electron-phonon interaction. The resulting method is applied to a one-level model system and a gold wire described by tight-binding model to demonstrate its validity and the importance of electron-phonon interaction for the quantum transport. As it is based on the effective single-electron model, the method can be readily extended to time-dependent density functional theory.

First-principles time-dependent quantum transport theory

A practical first-principles scheme for time-dependent transport through realistic systems at finite temperature is established by the combination of time-dependent density functional theory and nonequilibrium Green's-function formalism with wide-band limit approximation. This method extends the adiabatic wide-band limit approximation developed earlier [Zheng et al., Phys. Rev. B 75, 195127 (2007)]. It is implemented with both time-dependent density functional theory and time-dependent density functional tight-binding method and is applied to simulate the time-dependent transport through a carbon nanotube based electronic device to demonstrate its validity.

Time-dependent density functional theory for quantum transport

Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.

Spin-flip scattering in time-dependent transport through a quantum dot: Enhanced spin-current and inverse tunneling magnetoresistance

We study the effects of spin-flip scatterings on the time-dependent transport properties through a magnetic quantum dot attached to normal and ferromagnetic leads. The transient spin-dynamics as well as the steady-state tunneling magnetoresistance (TMR) of the system are investigated. The absence of a definite spin quantization axis requires the time-propagation of two-component spinors. We present numerical results in which the electrodes are treated both as one-dimensional tightbinding wires and in the wide-band limit approximation. In the latter case we derive a transparent analytic formula for the spin-resolved current, and transient oscillations damped over different timescales are identified. We also find a novel regime for the TMR inversion. For any given strength of the spin-flip coupling the TMR becomes negative provided the ferromagnetic polarization is larger than some critical value. Finally we show how the full knowledge of the transient response allows for enhancing the spin-current by properly tuning the period of a pulsed bias.

Time-dependent density-functional theory for open systems

By introducing the self-energy density functionals for the dissipative interactions between the reduced system and its environment, we develop a time-dependent density-functional theory formalism based on an equation of motion for the Kohn-Sham reduced single-electron density matrix of the reduced system. Two approximate schemes are proposed for the self-energy density functionals, the complete second order approximation and the wide-band limit approximation. A numerical method based on the wide-band limit approximation is subsequently developed and implemented to simulate the steady and transient current through various realistic molecular devices. Simulation results are presented and discussed.

Time-dependent quantum transport: Direct analysis in the time domain

We present a numerical approach for solving time-dependent quantum transport problems in molecular electronics. By directly solving Green's functions in the time domain, this approach does not rely on the wide-band limit approximation thereby is capable of taking into account the detailed electronic structures of the device leads which is important for molecular electronics. Using this approach we investigate two typical situations: current driven by a bias voltage pulse and by a periodic field, illustrating that the computational requirement is no more than an inversion of a relatively small triangular matrix plus several matrix multiplications. We then present numerical results of time-dependent charge current for a one-dimensional atomic chain. The numerical solution recovers known results in the wide-band limit, and reveals physical behavior for leads with finite bandwidth.

Influence of microwave fields on electron transport through a quantum dot in the presence of direct tunneling between leads

We consider the time-dependent electron transport through a quantum dot coupled to two leads in the presence of the additional over-dot (bridge) tunneling channel. By using the evolution operator method together with the wide-band limit approximation we derived the analytical formulaes for the quantum dot charge and current flowing in the system. The influence of the external microwave field on the time-average quantum dot charge, the current and the derivatives of the average current with respect to the gate and source-drain voltages has been investigated for a wide range of parameters.