Time-dependent Electron Transport Research Articles

(Invited) Scaling, Coarse Graining, and Bottlenecks on the Microstructural Modeling of Lithium-Ion Batteries

Historically, the properties of materials for rechargeable lithium-ion batteries, solid oxide fuel cells, and other energy-related applications has been investigated by self-consistently averaging the effect of an individual representative material feature and incorporating it into coarse grained (one-dimensional) descriptions that capture the time-dependent electronic and ionic transport. Such an approach is based on using analytic solutions of simplified representations of grains, pores, or inclusions, and averaging them into models that aim to understand or engineer the macroscopic properties of the device or component at hand. However, if effects due to phase transformation kinetics, or the impact of defects such as vacancies or interstitials, dislocations, or grain boundaries are to be engineered, currently used averaging approaches will not capture the underlying multiphysical and microstructural richness of behavior of the device. In general, the modern development of advanced technology for energy applications demands: 1) the formulation of a methodology that provides an accurate description of the materials that integrate these devices at each length scale; 2) the systematic and mindful coarse-graining of lower length scale methodologies into higher length scale descriptions, and 3) the establishment of meaningful databases that enable the development of insight to understand and then engineer advanced, reliable, next generation devices. Here, by defining a thermodynamically consistent representation of materials that spatially resolves the multiphysical fields that results from formally considering microstructural features such as grain size, crystallographic texture, grain boundaries, particle size, and porosity, the time-dependent galvanostatic behavior is analyzed in lithium-ion batteries. Progress towards integrating the physical contributions of each individual phase and its processing-induced spatial distribution into advanced homogenized models is presented. The effect on the performance and degradations is analyzed. Reaches and limitations of well-known and emerging theories will be reviewed and compared, and efforts to accelerate to the limit of real time performance and degradation computations will be presented in an effort to explore the space of what is physically possible.

Electric Current Fluctuations Induced by Molecular Vibrations in the Adiabatic Limit: Molecular Dynamics-Driven Liouville von Neumann Approach

We investigate time-dependent electron transport through a molecular junction in the adiabatic limit at the density-functional tight-binding level using the molecular dynamics-driven Liouville von ...

Buildup of vibron-mediated electron correlations in molecular junctions

We investigate on the same footing the time-dependent electronic transport properties and vibrational dynamics of a molecular junction. We show that fluctuations of both the molecular vibron displacement and the electronic current across the junction undergo damped oscillations towards the steady-state. We assign the former to the onset of electron tunneling events assisted by vibron-emission. The time-dependent build-up of electron-hole correlations is revealed as a departure of the charge-transfer statistics from the generalized-binomial one after a critical time tc. The phonon-back action on the tunneling electrons is shown to amplify and accelerate this build-up mechanism.

Time-dependent Electron Acceleration in Pulsar Wind Termination Shocks: Application to the 2011 April Crab Nebula Gamma-Ray Flare

Abstract The γ-ray flares from the Crab Nebula observed by AGILE and Fermi-LAT between 2007 and 2013 reached GeV photon energies and lasted several days. The strongest emission, observed during the 2011 April “superflare”, exceeded the quiescent level by more than an order of magnitude. These observations challenge the standard models for particle acceleration in pulsar wind nebulae, because the radiating electrons have energies exceeding the classical radiation-reaction limit for synchrotron emission. Particle-in-cell simulations have suggested that the classical synchrotron limit can be exceeded if the electrons also experience electrostatic acceleration due to shock-driven magnetic reconnection. In this paper, we revisit the problem using an analytic approach based on solving a fully time-dependent electron transport equation describing the electrostatic acceleration, synchrotron losses, and escape experienced by electrons in a magnetically confined plasma “blob” as it encounters and passes through the pulsar wind termination shock. We show that our model can reproduce the γ-ray spectra observed during the rising and decaying phases of each of the two sub-flare components of the 2011 April superflare. We integrate the spectrum for photon energies MeV to obtain the light curve for the event, which also agrees with the observations. We find that strong electrostatic acceleration occurs on both sides of the termination shock, driven by magnetic reconnection. We also find that the dominant mode of particle escape changes from diffusive escape to advective escape as the blob passes through the shock.

Communication: Master equations for electron transport: The limits of the Markovian limit.

Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs"-explicit degrees of freedom associated with the electrodes-distinguishing them from many previous classes of master equations. Starting from a Lindblad equation, we develop a common foundation for these approaches. Due to the incorporation of explicit electrode states, these methods do not require a large bias or even "true Markovianity" of the reservoirs. Nonetheless, their predictions are only physically relevant when the Markovian relaxation is weaker than the thermal broadening and when the extended reservoirs are "sufficiently large," in a sense that we quantify. These considerations hold despite complete positivity and respect for Pauli exclusion at any relaxation strength.

Shot noise in a harmonically driven ballistic graphene transistor

We study time-dependent electron transport and quantum noise in a ballistic graphene field effect transistor driven by an ac gate potential. The non-linear response to the ac signal is computed through Floquet theory for scattering states and Landauer-B\"uttiker theory for charge current and its fluctuations. Photon-assisted excitation of a quasibound state in the top-gate barrier leads to resonances in transmission that strongly influence the noise properties. For strong doping of graphene under source and drain contacts, when electrons are transmitted through the channel via evanescent waves, the resonance leads to a substantial suppression of noise. The Fano factor is then reduced well below the pseudo-diffusive value, $F<1/3$, also for strong ac drive. The good signal-to-noise ratio (small Fano factor) on resonance suggests that the device is a good candidate for high-frequency (THz) radiation detection. We show analytically that Klein tunneling (total suppression of back-reflection) persists for perpendicular incidence also when the barrier is driven harmonically. Although the transmission is inelastic and distributed among sideband energies, a sum rule leads to total suppression of shot noise.

Nonlinear response of a ballistic graphene transistor with an ac-driven gate: High harmonic generation and terahertz detection

We present results for time-dependent electron transport in a ballistic graphene field-effect transistor with an ac-driven gate. Nonlinear response to the ac drive is derived utilizing Floquet theory for scattering states in combination with Landauer-B\"uttiker theory for transport. We identify two regimes that can be useful for applications: (i) low and (ii) high doping of graphene under source and drain contacts, relative to the doping level in the graphene channel, which in an experiment can be varied by a back gate. In both regimes, inelastic scattering induced by the ac drive can excite quasi-bound states in the channel that leads to resonance promotion of higher order sidebands. Already for weak to intermediate ac drive strength, this leads to a substantial change in the direct current between source and drain. For strong ac drive with frequency $\Omega$, we compute the higher harmonics of frequencies $n\Omega$ ($n$ integer) in the source-drain conductance. In regime (ii), we show that particular harmonics (for instance $n=6$) can be selectively enhanced by tuning the doping level in the channel or by tuning the drive strength. We propose that the device operated in the weak-drive regime can be used to detect THz radiation, while in the strong-drive regime it can be used as a frequency multiplier.

Transparent boundary conditions for time-dependent electron transport in the [formula omitted]-matrix method with applications to nanostructured interfaces

Transparent boundary conditions for the time-dependent Schrödinger equation are implemented using the R-matrix method. The employed scattering formalism is suitable for describing open quantum systems and provides the framework for the time-dependent coherent transport. Transmission and reflection of wave functions at the edges of a finite quantum system are essential for an accurate and efficient description of the time-dependent processes on large time scales. We detail the computational method and point out the numerical advantages stemming from the open system approach based on the R-matrix formalism. The approach is used here to describe time-dependent transport across nanostructured interfaces relevant for photovoltaic applications.

Reprint of : Time dependent electronic transport in chiral edge channels

We study time dependent electronic transport along the chiral edge channels of the quantum Hall regime, focusing on the role of Coulomb interaction. In the low frequency regime, the a.c. conductance can be derived from a lumped element description of the circuit. At higher frequencies, the propagation equations of the Coulomb coupled edge channels need to be solved. As a consequence of the interchannel coupling, a charge pulse emitted in a given channel fractionalized in several pulses. In particular, Coulomb interaction between channels leads to the fractionalization of a charge pulse emitted in a given channel in several pulses. We finally study how the Coulomb interaction, and in particular the fractionalization process, affects the propagation of a single electron in the circuit. All the above-mentioned topics are illustrated by experimental realizations.

Time dependent electronic transport in chiral edge channels

We study time dependent electronic transport along the chiral edge channels of the quantum Hall regime, focusing on the role of Coulomb interaction. In the low frequency regime, the a.c. conductance can be derived from a lumped element description of the circuit. At higher frequencies, the propagation equations of the Coulomb coupled edge channels need to be solved. As a consequence of the interchannel coupling, a charge pulse emitted in a given channel fractionalized in several pulses. In particular, Coulomb interaction between channels leads to the fractionalization of a charge pulse emitted in a given channel in several pulses. We finally study how the Coulomb interaction, and in particular the fractionalization process, affects the propagation of a single electron in the circuit. All the above-mentioned topics are illustrated by experimental realizations.

Single-electron approach for time-dependent electron transport

We developed a new approach to electron transport in mesoscopic systems by using a particular single-particle basis. Although this basis generates redundant many-particle amplitudes, it greatly simplifies the treatment. By using our method for transport of non-interacting electrons, we generalize the Landauer formula for transient currents and time-dependent potentials. The result has a very simple form and clear physical interpretation. As an example, we apply it to resonant tunneling through a quantum dot where the tunneling barriers are oscillating in time. We obtain an analytical expression for the time-dependent (ac) resonant current. However, in the adiabatic limit this expression displays the dc current for zero bias (electron pumping).

Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations

A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.

Dissipative time-dependent quantum transport theory: Quantum interference and phonon induced decoherence dynamics.

A time-dependent inelastic electron transport theory for strong electron-phonon interaction is established via the equations of motion method combined with the small polaron transformation. In this work, the dissipation via electron-phonon coupling is taken into account in the strong coupling regime, which validates the small polaron transformation. The corresponding equations of motion are developed, which are used to study the quantum interference effect and phonon-induced decoherence dynamics in molecular junctions. Numerical studies show clearly quantum interference effect of the transport electrons through two quasi-degenerate states with different couplings to the leads. We also found that the quantum interference can be suppressed by the electron-phonon interaction where the phase coherence is destroyed by phonon scattering. This indicates the importance of electron-phonon interaction in systems with prominent quantum interference effect.

Wave-packet representation of leads for efficient simulations of time-dependent electronic transport

We present theoretical foundations and numerical demonstration of an efficient method for performing time-dependent many-electron simulations for electronic transport. The method employs the concept of stroboscopic wavepacket basis for the description of electrons' dynamics in the semi-infinite leads.The rest of the system can be treated using common propagation schemes for finite electronic systems. We use the implementation of our method to study the time-dependent current response in armchair graphene nano-ribbons (AGNR) with sizes up to 800 atoms described within tight-binding approximation. The character of the time-dependent current is studied for different magnitudes of the bias voltage, variable width and length of AGNRs, different positions of the current measurement, and for full and reduced coupling of the AGNRs to the electrodes.

Time-dependent density-functional theory for open electronic systems

Time-dependent density-functional theory (TDDFT) has been successfully applied to predict excited-state properties of isolated and periodic systems. However, it cannot address a system coupled to an environment or whose number of electrons is not conserved. To tackle these problems, TDDFT needs to be extended to accommodate open systems. This paper provides a comprehensive account of the recent developments of TDDFT for open systems (TDDFT-OS), including both theoretical and practical aspects. The practicality and accuracy of a latest TDDFT-OS method is demonstrated with two numerical examples: the time-dependent electron transport through a series of quasi-one-dimensional atomic chains, and the real-time electronic dynamics on a two-dimensional graphene surface. The advancement of TDDFT-OS may lead to promising applications in various fields of chemistry, including energy conversion and heterogeneous catalysis.

Time-dependent electron transport through a strongly correlated quantum dot: multiple-probe open-boundary conditions approach

We present a time-dependent study of electron transport through a strongly correlated quantum dot, which combines adiabatic lattice density functional theory in the Bethe ansatz local-density approximation (BALDA) to the Hubbard model, with the multiple-probe battery method for open-boundary simulations in the time domain. In agreement with the recently proposed dynamical picture of Coulomb blockade, a characteristic driven regime, defined by regular current oscillations, is demonstrated for a certain range of bias voltages. We further investigate the effects of systematically improving the approximation for the electron–electron interaction at the dot site (going from non-interacting, through Hartree-only to adiabatic BALDA) on the transmission spectrum and the I–V characteristics. In particular, a negative differential conductance is obtained at large bias voltages and large Coulomb interaction strengths. This is attributed to the combined effect of the electron–electron interaction at the dot and the finite bandwidth of the electrodes.

Magnetic-field-influenced nonequilibrium transport through a quantum ring with correlated electrons in a photon cavity

We investigate magnetic-field influenced time-dependent transport of Coulomb interacting electrons through a two-dimensional quantum ring in an electromagnetic cavity under non-equilibrium conditions described by a time-convolutionless non-Markovian master equation formalism. We take into account the full electromagnetic interaction of electrons and cavity photons without resorting to the rotating wave approximation or reduction to two levels. A bias voltage is applied to semi-infinite leads along the x-axis, which are connected to the quantum ring. The magnetic field is tunable to manipulate the time-dependent electron transport coupled to a photon field with either x- or y-polarization. We find that the lead-system-lead current is strongly suppressed by the y-polarized photon field at magnetic field with two flux quanta due to a degeneracy of the many-body energy spectrum of the mostly occupied states. Furthermore, the current can be significantly enhanced by the y-polarized field at magnetic field with half integer flux quanta.

Spin transport and tunable Gilbert damping in a single-molecule magnet junction

We study time-dependent electronic and spin transport through an electronic level connected to two leads and coupled with a single-molecule magnet via exchange interaction. The molecular spin is treated as a classical variable and precesses around an external magnetic field. We derive expressions for charge and spin currents by means of the Keldysh non-equilibrium Green's functions technique in linear order with respect to the time-dependent magnetic field created by this precession. The coupling between the electronic spins and the magnetization dynamics of the molecule creates inelastic tunneling processes which contribute to the spin currents. The inelastic spin currents, in turn, generate a spin-transfer torque acting on the molecular spin. This back-action includes a contribution to the Gilbert damping and a modification of the precession frequency. The Gilbert damping coefficient can be controlled by the bias and gate voltages or via the external magnetic field and has a non-monotonic dependence on the tunneling rates.

Intrinsic oscillations of spin current polarization in a paramagnetic resonant tunneling diode

A spin- and time-dependent electron transport has been studied in a paramagnetic resonant tunneling diode using the self-consistent Wigner-Poisson method. Based on the calculated current-voltage characteristics in an external magnetic field, we have demonstrated that under a constant bias both the spin-up and spin-down current components exhibit the THz oscillations in two different bias voltage regimes. We have shown that the oscillations of the spin-up (down) polarized current result from the coupling between the two resonance states: one localized in the triangular quantum well created in the emitter region and the second localized in the main quantum well. We have also elaborated the one-electron model of the current oscillations, which confirms the results obtained with the Wigner-Poisson method. The spin current oscillations can lower the effectiveness of spin filters based on the paramagnetic resonant tunneling structures and can be used to design the generators of the spin polarized current THz oscillations that can operate under the steady bias and constant magnetic field.

Nonadiabatic electron pumping through interacting quantum dots

We study non-adiabatic charge pumping through single-level quantum dots taking into account Coulomb interactions. We show how a truncated set of equations of motion can be propagated in time by means of an auxiliary-mode expansion. This formalism is capable of treating the time-dependent electronic transport for arbitrary driving parameters. We verify that the proposed method describes very precisely the well-known limit of adiabatic pumping through quantum dots without Coulomb interactions. As an example we discuss pumping driven by short voltage pulses for various interaction strengths. Such finite pulses are particular suited to investigate transient non-adiabatic effects, which may be also important for periodic drivings, where they are much more difficult to reveal.