Time-dependent Quantum Transport Research Articles

Theoretical Study for Carrier Transit Limited Performance of Gate-All-Around Si Nanowire Transistor by Time-Dependent Quantum Transport Simulation

Theoretically, the upper limit performance of nanoscale transistor should be limited by carrier transit time through the channel as the charge in channel cannot follow the gate voltage and the gate capacitance will show strong frequency dependence if the gate voltage varies faster than the carrier transit time. Currently, the operation frequency of nanoscale transistor is limited by the non-ideal factors such as parasitic effects, and it is far below the limit caused by carrier transit time. However, how good the transistor can be if one can minimize these non-ideal factors is still a problem, thus, it would be worth exploring its upper limit performance. In this article, time-dependent quantum transport simulation is performed to explore the carrier transit limited performance of the gate-all-around (GAA) Si nanowire transistor. By using the mode space approach, the 3-D time-dependent quantum transport equation is decoupled to a 2-D confinement problem and a 1-D transport problem, and then self-consistently solved with the Poisson’s equation. The transient characteristics of channel charge are investigated, and it shows the response time of channel charge is in the scale of 0.1 ps. The responses of channel charge and drain current to high-frequency gate voltages are simulated. The carrier transit limited performance including the frequency-dependent gate capacitance and transconductance, 3 dB bandwidth, and cutoff frequency, are calculated and discussed.

Tkwant: a software package for time-dependent quantum transport

Tkwant is a Python package for the simulation of quantum nanoelectronics devices to which external time-dependent perturbations are applied. Tkwant is an extension of the kwant package (https://kwant-project.org/) and can handle the same types of systems: discrete tight-binding-like models that consist of an arbitrary central region connected to semi-infinite electrodes. The problem is genuinely many-body even in the absence of interactions and is treated within the non-equilibrium Keldysh formalism. Examples of Tkwant applications include the propagation of plasmons generated by voltage pulses, propagation of excitations in the quantum Hall regime, spectroscopy of Majorana fermions in semiconducting nanowires, current-induced skyrmion motion in spintronic devices, multiple Andreev reflection, Floquet topological insulators, thermoelectric effects, and more. The code has been designed to be easy to use and modular. Tkwant is free software distributed under a BSD license and can be found at https://tkwant.kwant-project.org/.

A computational approach for investigating Coulomb interaction using Wigner\u2013Poisson coupling

Entangled quantum particles, in which operating on one particle instantaneously influences the state of the entangled particle, are attractive options for carrying quantum information at the nanoscale. However, fully-describing entanglement in traditional time-dependent quantum transport simulation approaches requires significant computational effort, bordering on being prohibitive. Considering electrons, one approach to analyzing their entanglement is through modeling the Coulomb interaction via the Wigner formalism. In this work, we reduce the computational complexity of the time evolution of two interacting electrons by resorting to reasonable approximations. In particular, we replace the Wigner potential of the electron–electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential. It is demonstrated that for some particular configurations of an electron–electron system, the introduced approximations are feasible. Purity, identified as the maximal coherence for a quantum state, is also analyzed and its corresponding analysis demonstrates that the entanglement due to the Coulomb interaction is well accounted for by the introduced local approximation.

Magnon-driven chiral charge and spin pumping and electron-magnon scattering from time-dependent quantum transport combined with classical atomistic spin dynamics

Using newly developed quantum-classical hybrid framework, we investigate interaction between spin-polarized conduction electrons and a single spin wave (SW) coherently excited within a metallic ferromagnetic nanowire. When the nanowire hosting SW is attached to two normal metal (NM) leads, with no dc bias voltage applied between them, the SW pumps chiral electronic charge and spin currents into the leads---their direction is tied to the direction of SW propagation and they scale linearly with the frequency of the precession. This is in contrast to: standard pumping by the uniform precession mode with identical spin currents flowing in both directions and no accompanying charge current; or experimentally observed [C.~Ciccarelli et al., Nat. Nanotech. 10, 50 (2014); M.~Evelt et al., Phys. Rev. B 95, 024408 (2017)] magnonic charge pumping which requires spin-orbit coupling spin-orbit coupling. The mechanism behind our prediction is nonadiabaticity due to time-retardation effects---motion of localized magnetic moment affects conduction electron spin in a retarded way, so that it takes a finite time until the electron spin reacts to the motion of the classical vector. Upon injecting dc spin-polarized charge current from the left NM lead, electrons interact with SW where outflowing charge and spin current into the right NM lead are changed due to both scattering off time-dependent potential generated by the SW and superposition with the currents pumped by the SW itself. Using Lorentzian voltage pulse to excite leviton out of the Fermi sea, which carries one electron charge with no accompanying electron-hole pairs and behaves as soliton-like quasiparticle, we describe how a single electron interacts with a single SW.

Time-dependent quantum transport in the presence of elastic scattering

Abstract A time-dependent quantum transport model considering elastic scattering is proposed. The model, solves the time-dependent Schrodinger equation in the presence of scattering. Inspired by the non-equilibrium Green's function (NEGF) method, an imaginary potential is added to the time-dependent Schrodinger equation for absorbing electron waves and a source term to model the injection of electron waves. The value of the imaginary potential is chosen so that the total probability density of the waves is conserved. A perfect absorber boundary condition is used to prevent wave reflection from boundaries in all the simulations. To verify the accuracy of the model, the results are compared with those of other methods in different scenarios. In a simple scenario where the quantum effects are not so significant, our results are close to those obtained from Boltzmann transport equation. In another scenario which uses a potential profile like a resonant tunneling diode, the results in the steady-state conditions are close to those obtained from NEGF method in self-consistent Born approximation. Moreover, the transmission chart for a resonant structure in the steady-state conditions shows that decoherence is well included in the proposed model.

Timescale separation solution of the Kadanoff-Baym equations for quantum transport in time-dependent fields

The interaction with time-dependent external fields, especially the interplay between time-dependent driving and quantum correlations, changes the familiar picture of electron transport through nanoscale systems. Although the exact solution of the problem of AC quantum transport of noninteracting electrons has been known for more than two decades, the treatment of correlated particles presents a significant theoretical challenge. In this paper, using the perturbative separation of fast electron tunnelling and slow driving time-scales, we developed a practical approach for time-dependent quantum transport with nonequilibrium Green's functions. The fast electronic dynamics is associated with relative time whilst the slow driving is related to the central time in the Green's functions. The ratio of characteristic electron tunneling time over the period of harmonic driving is used as a small parameter in the theory to obtain a convergent time-derivative expansions of the Green's functions. This enables the algebraic solution of the Kadanoff-Baym equations in Wigner space. Consequently, we produced analytical expressions for dynamical corrections to advanced, retarded, and lesser Green's functions, as well as an improved expression for AC electric current. The method developed is applicable to the general case of multi-channel electron transport through a correlated central region. The theory is applied to different transport scenarios: time-dependent transport through a driven single-resonant level is compared to exact results; and electron transport through a molecular junction described by the Holstein model with a time-oscillating voltage bias is also investigated.

Quantum dynamics of single-photon detection using functionalized quantum transport electronic channels

Single photon detectors have historically consisted of macroscopic-sized materials but recent experimental and theoretical progress suggests new approaches based on nanoscale and molecular electronics. Here we present a theoretical study of photodetection in a system composed of a quantum electronic transport channel functionalized by a photon absorber. Notably, the photon field, absorption process, transduction mechanism, and measurement process are all treated as part of one fully-coupled quantum system, with explicit interactions. Using non-equilibrium, time-dependent quantum transport simulations, we reveal the unique temporal signatures of the single photon detection process, and show that the system can be described using optical Bloch equations, with a new non-linearity as a consequence of time-dependent detuning caused by the backaction from the transport channel via the dynamical Stark effect. We compute the photodetector signal-to-noise ratio and demonstrate that single photon detection at high count rate is possible for realistic parameters by exploiting a novel non-equilibrium control of backaction.

CHEERS: a tool for correlated hole-electron evolution from real-time simulations

We put forward a practical nonequilibrium Green’s function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff–Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree–Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed.

Controlling observables in normal, hybrid and Josephson junctions

ABSTRACTThe theory of time-dependent quantum transport addresses the question: How do electrons flow through a junction under the influence of an external perturbation as time goes by? In this article, we invert this question and search for a time-dependent bias such that the system behaves in a desired way. Our system of choice consists of quantum dots coupled to normal or superconducting leads. We present results for junctions with normal leads where the current, the density or a molecular vibration is optimised to follow a given target pattern. For junctions with two superconducting leads, where the Josephson effect triggers the current to oscillate, we investigate what happens if the frequency of the Josephson oscillation comes close to the frequency of the molecular vibration. Furthermore we show how to suppress the Josephson oscillations by suitably tailoring the bias. In a second example involving superconductivity, we consider a Y-shaped junction with two quantum dots coupled to one superconducting and two normal leads. This device is used as a Cooper pair splitter to create entangled electrons on the two quantum dots. We maximise the splitting efficiency with the help of an optimised bias.

Theory of quantum transport in disordered systems driven by voltage pulse

Predicting time-dependent quantum transport in the transient regime is important for understanding the intrinsic dynamic response of a nanodevice and for predicting the limit of how such a device can switch on or off a current. Theoretically, this problem becomes quite difficult to solve when the nanodevice contains disorder because the calculated transient current must be averaged over many disorder configurations. In this work, we present a theoretical formalism to calculate the configuration averaged time-dependent current flowing through a phase coherent device containing disorder sites where the transient current is driven by sharply turning on and off the external bias voltage. Our theory is based on the Keldysh nonequilibrium Green's function (NEGF) formalism and is applicable in the far from equilibrium nonlinear response quantum transport regime. The effects of disorder scattering are dealt with by the coherent potential approximation (CPA) extended in the time domain. We show that after approximations such as CPA and vertex corrections for calculating the multiple impurity scattering in the transient regime, the derived NEGFs perfectly satisfy a Ward identity. The theory is quantitatively verified by comparing its predictions to the exact solution for a tight-binding model of a disordered two-probe transport junction.

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.

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport.

Based on the complex absorbing potential (CAP) method, a Lorentzian expansion scheme is developed to express the self-energy. The CAP-based Lorentzian expansion of self-energy is employed to solve efficiently the Liouville-von Neumann equation of one-electron density matrix. The resulting method is applicable for both tight-binding and first-principles models and is used to simulate the transient currents through graphene nanoribbons and a benzene molecule sandwiched between two carbon-atom chains.

Time-dependent Landauer-Büttiker formula: Application to transient dynamics in graphene nanoribbons

In this work we develop a time-dependent extension of the Landauer-B\"uttiker approach to study transient dynamics in time-dependent quantum transport through molecular junctions. A key feature of the approach is that it provides a closed integral expression for the time-dependence of the density matrix of the molecular junction after switch-on of a bias or gate potential which can be evaluated without the necessity of propagating individual single-particle orbitals. This allows for the study of time-dependent transport in large molecular systems coupled to wide band leads. As an application of the formalism we study the transient dynamics of zigzag and armchair graphene nanoribbons of different symmetries. We find that the transient times can exceed several hundreds of femtoseconds while displaying a long time oscillatory motion related to multiple reflections of the density wave in the nanoribbons at the ribbon--lead interface. This temporal profile has a shape that scales with the length of the ribbons and is modulated by fast oscillations described by intra-ribbon and ribbon--lead transitions. Especially in the armchair nanoribbons there exists a sequence of quasi-stationary states related to reflections at the edge state located at the ribbon--lead interface. In the case of zigzag nanoribbons there is a predominant oscillation frequency associated with virtual transitions between the edge states and the Fermi levels of the electrode. We further study the local bond currents in the nanoribbons and find that the parity of the edges strongly affects the path of the electrons in the nanoribbons. We finally study the behavior of the transients for various added gate potentials.

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.

Application of hierarchical equations of motion (HEOM) to time dependent quantum transport at zero and finite temperatures

Going beyond the limitations of our earlier works [X. Zheng, F. Wang, C.Y. Yam, Y. Mo, G.H. Chen, Phys. Rev. B 75, 195127 (2007); X. Zheng, G.H. Chen, Y. Mo, S.K. Koo, H. Tian, C.Y. Yam, Y.J. Yan, J. Chem. Phys. 133, 114101 (2010)], we propose, in this manuscript, a new alternative approach to simulate time-dependent quantum transport phenomenon from first-principles. This new practical approach, still retaining the formal exactness of HEOM framework, does not rely on any intractable parametrization scheme and the pole structure of Fermi distribution function, thus, can seamlessly incorporated into first-principles simulation and treat transient response of an open electronic systems to an external bias voltage at both zero and finite temperatures on the equal footing. The salient feature of this approach is surveyed, and its time complexity is analysed. As a proof-of-principle of this approach, simulation of the transient current of one dimensional tight-binding chain, driven by some direct external voltages, is demonstrated.

Gauge-invariant and current-continuous microscopic ac quantum transport theory

There had been consensus on what the accurate ac quantum transport theory was until some recent works challenged the conventional wisdom. Basing on the non-equilibrium Green's function formalism for time-dependent quantum transport, we derive an expression for the dynamic admittance that satisfies gauge invariance and current continuity, and clarify the key concept in the field. The validity of our now formalism is verified by first-principles calculation of the transient current through a carbon-nanotube-based device under the time-dependent bias voltage. Moreover, the previously well-accepted expression for dynamic admittance is recovered only when the device is a perfect conductor at a specific potential.

Time-dependent density functional theory for quantum transport

The rapid miniaturization of electronic devices motivates research interests in quantum transport. Recently time-dependent quantum transport has become an important research topic. Here we review recent progresses in the development of time-dependent density-functional theory for quantum transport including the theoretical foundation and numerical algorithms. In particular, the reduced-single electron density matrix based hierarchical equation of motion, which can be derived from Liouville-von Neumann equation, is reviewed in details. The numerical implementation is discussed and simulation results of realistic devices will be given.

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.