Time-dependent Nonequilibrium Green Function Research Articles

Spatio-temporal dynamics of shift current quantum pumping by femtosecond light pulse

Shift current—a photocurrent induced by light irradiating noncentrosymmetric materials in the absence of any bias voltage or built-in electric field—is one of the mechanisms of the so-called bulk photovoltaic effect. It has been traditionally described as a nonlinear optical response of a periodic solid to continuous wave light using a perturbative formula, which is linear in the intensity of light and which involves Berry connection describing the shift in the center of mass position of the Wannier wave function associated with the transition between the valence and conduction bands of the solid. Since shift current is solely due to off-diagonal elements of the nonequilibrium density matrix that encode quantum correlations, its peculiar space–time dynamics in response to femtosecond light pulse employed locally can be expected. To study such response requires to analyze realistic two-terminal devices, instead of traditional periodic solids, for which we choose paradigmatic Rice–Mele model sandwiched between two metallic electrodes and apply to it time-dependent nonequilibrium Green function algorithms scaling linearly in the number of time steps and capable of treating nonperturbative effects in the amplitude of external time-dependent fields. This reveals novel features: superballistic transport, signified by time dependence of the displacement, ∼tν with ν > 1, of the photoexcited charge carriers from the spot where the femtosecond light pulse is applied toward the electrodes; and photocurrent quadratic in light intensity at subgap frequencies of light due to two-photon absorption processes that were missed in previous perturbative analyses. Furthermore, frequency dependence of the DC component of the photocurrent reveals shift current as a realization of nonadiabatic quantum charge pumping enabled by breaking of left–right symmetry of the device structure. This demonstrates that a much wider class of systems, than the usually considered polar noncentrosymmetric bulk materials, can be exploited to generate nonzero DC component of photocurrent in response to unpolarized light and optimize shift-current-based solar cells and optoelectronic devices.

Spin and Charge Pumping by a Steady or Pulse-Current-Driven Magnetic Domain Wall: A Self-Consistent Multiscale Time-Dependent Quantum-Classical Hybrid Approach

We introduce a multiscale framework which combines time-dependent nonequilibrium Green function (TD-NEGF) algorithms, scaling linearly in the number of time steps and describing quantum-mechanically conduction electrons in the presence of time-dependent fields of arbitrary strength or frequency, with classical time evolution of localized magnetic moments described by the Landau-Lifshitz-Gilbert (LLG) equation. The TD-NEGF+LLG framework can be applied to a variety of problems where current-driven spin torque induces dynamics of magnetic moments as the key resource for next generation spintronics. Using magnetic domain wall (DW) as an example, we predict that its motion will pump time-dependent spin and charge currents (on the top of unpolarized DC charge current injected through normal metal leads to drive the DW motion). The conversion of AC components of spin current, whose amplitude increases (decreases) as the DW approaches (distances from) the normal metal lead, into AC voltage via the inverse spin Hall effect offers a tool to precisely track the DW position along magnetic nanowire. We also quantify the DW transient inertial displacement due to its acceleration and deceleration by pulse current and the entailed spin and charge pumping. Finally, TD-NEGF+LLG as a nonperturbative (i.e., numerically exact) framework allows us to establish the limits of validity of the so-called spin-motive force (SMF) theory for pumped charge current by time-dependent magnetic textures---the perturbative analytical formula of SMF theory becomes inapplicable for large frequencies (but unrealistic in magnetic system) and, more importantly, for increasing noncollinearity when the angles between neighboring magnetic moments exceed $\simeq 10^\circ$.

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.

When can time-dependent currents be reproduced by the Landauer steady-state approximation?

We establish well-defined limits in which the time-dependent electronic currents across a molecular junction subject to a fluctuating environment can be quantitatively captured via the Landauer steady-state approximation. For this, we calculate the exact time-dependent non-equilibrium Green's function (TD-NEGF) current along a model two-site molecular junction, in which the site energies are subject to correlated noise, and contrast it with that obtained from the Landauer approach. The ability of the steady-state approximation to capture the TD-NEGF behavior at each instant of time is quantified via the same-time correlation function of the currents obtained from the two methods, while their global agreement is quantified by examining differences in the average currents. The Landauer steady-state approach is found to be a useful approximation when (i) the fluctuations do not disrupt the degree of delocalization of the molecular eigenstates responsible for transport and (ii) the characteristic time for charge exchange between the molecule and leads is fast with respect to the molecular correlation time. For resonant transport, when these conditions are satisfied, the Landauer approach is found to accurately describe the current, both on average and at each instant of time. For non-resonant transport, we find that while the steady-state approach fails to capture the time-dependent transport at each instant of time, it still provides a good approximation to the average currents. These criteria can be employed to adopt effective modeling strategies for transport through molecular junctions in interaction with a fluctuating environment, as is necessary to describe experiments.

Spin-orbit torque-driven magnetization switching in 2D-topological insulator heterostructure

Charge pumping and spin-orbit torque (SOT) are two reciprocal phenomena widely studied in ferromagnet (FM)/topological insulator (TI) heterostructures. However, the SOT and its corresponding switching phase diagram for a FM island in proximity to a two-dimensional topological insulator (2DTI) has not been explored yet. We have addressed these features, using the recently developed adiabatic expansion of time-dependent nonequilibrium Green's function (NEGF) in the presence of both precessing magnetization and bias voltage. We have calculated the angular and spatial dependence of different components of the SOT on the FM island. We determined the switching phase diagram of the FM for different orientations of the easy axis. The results can be used as a guideline for the future experiments on such systems.

Efficient auxiliary-mode approach for time-dependent nanoelectronics

A new scheme for numerically solving the equations arising in the time-dependent non-equilibrium Green's function formalism is developed. It is based on an auxiliary-mode expansion of the self-energies which convert the complicated set of integro-differential equations into a set of ordinary differential equations. In the new scheme all auxiliary matrices are replaced by vectors or scalars. This drastically reduces the computational effort and memory requirements of the method, rendering it applicable to topical problems in electron quantum optics and molecular electronics. As an illustrative example we consider the dynamics of a Leviton wave-packet in a 1D wire.

Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach

Motivated by recent experiments observing spin-orbit torque (SOT) acting on the magnetization $\stackrel{P\vec}{m}$ of a ferromagnetic (F) overlayer on the surface of a three-dimensional topological insulator (TI), we investigate the origin of the SOT and the magnetization dynamics in such systems. We predict that lateral F/TI bilayers of finite length, sandwiched between two normal metal leads, will generate a large anti-damping-like SOT per very low charge current injected parallel to the interface. The large values of anti-damping-like SOT are spatially localized around the transverse edges of the F overlayer. Our analysis is based on adiabatic expansion (to first order in $\ensuremath{\partial}\stackrel{P\vec}{m}/\ensuremath{\partial}t$) of time-dependent nonequilibrium Green functions (NEGFs), describing electrons pushed out of equilibrium both by the applied bias voltage and by the slow variation of a classical degree of freedom [such as $\stackrel{P\vec}{m}(t)$]. From it we extract formulas for spin torque and charge pumping, which show that they are reciprocal effects to each other, as well as Gilbert damping in the presence of SO coupling. The NEGF-based formula for SOT naturally splits into four components, determined by their behavior (even or odd) under the time and bias voltage reversal. Their complex angular dependence is delineated and employed within Landau-Lifshitz-Gilbert simulations of magnetization dynamics in order to demonstrate capability of the predicted SOT to efficiently switch $\stackrel{P\vec}{m}$ of a perpendicularly magnetized F overlayer.

Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state

The nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by a generalized Holstein model is presented. A combination of methodologies, including the reduced density matrix formalism, the multilayer multiconfiguration time-dependent Hartree method, and a time-dependent nonequilibrium Green's function approach, is used to explore the transient behavior on multiple time scales as the system approaches steady state. The dot population dynamics on short to intermediate times is governed by the dot-lead hybridization parameter ($\ensuremath{\Gamma}$) and by the typical phonon frequency (${\ensuremath{\omega}}_{c}$) and depends on the location of the energy level of the dot relative to the bias window. At longer times, the dynamics shows a distinct behavior depending on whether the system is in the adiabatic or nonadiabatic regime, with a quantum dot occupation that may depend on the initial preparation of the phonon degrees of freedom. A ``phase'' diagram of this effect as a function of the polaron shift ($\ensuremath{\lambda}$) for various phonon frequencies is derived, suggesting the existence of bistability on experimentally observable time scales.

Charge pumping by magnetization dynamics in magnetic and semimagnetic tunnel junctions with interfacial Rashba or bulk extrinsic spin-orbit coupling

We develop a time-dependent nonequilibrium Green function (NEGF) approach to the problem of spin pumping by precessing magnetization in one of the ferromagnetic layers within F$|$I$|$F magnetic tunnel junctions (MTJs) or F$|$I$|$N semi-MTJs in the presence of intrinsic Rashba spin-orbit coupling (SOC) at the F$|$I interface or the extrinsic SOC in the bulk of F layers of finite thickness (F, ferromagnet; N, normal metal; I, insulating barrier). To express the time-averaged pumped charge current, or the corresponding dc voltage signal in an open circuit, we construct a novel solution to double-time-Fourier-transformed NEGF equations. The two energy arguments of NEGFs in this representation are connected by the Floquet theorem describing multiphoton emission and absorption processes. Within this fully quantum-mechanical treatment of the conduction electrons, we find that (i) only in the presence of the interfacial Rashba SOC, the nonzero dc pumping voltage ${V}_{\mathrm{pump}}$ in F$|$I$|$N junctions can emerge at the adiabatic level (i.e., proportional to the microwave frequency), which could explain recent experiments on microwave-driven semi-MTJs [T. Moriyama et al., Phys. Rev. Lett. 100, 067602 (2008)]; (ii) a unique signature of this charge pumping phenomenon, where the Rashba SOC within the precessing F layer participates in the pumping process, is a ${V}_{\mathrm{pump}}$ that changes sign as the function of the precession cone angle; (iii) unlike conventional spin pumping in MTJs in the absence of any SOC, where one emitted or absorbed microwave photon is sufficient to match the exact solution in the frame rotating with the magnetization, the presence of the Rashba SOC requires taking into account up to 10 photons in order to reach the asymptotic value of pumped charge current; (iv) the disorder within F$|$I$|$F MTJs can enhance ${V}_{\mathrm{pump}}$ in the quasiballistic transport regime; and (v) the extrinsic SOC in F$|$I$|$F MTJs causes spin relaxation and eventually the decay of ${V}_{\mathrm{pump}}$, which becomes negligible when the ratio of F layer thickness to the spin-diffusion length is around five. Our formalism can also be applied to charge and spin propagation in any noninteracting open quantum system that is brought out of equilibrium by time-dependent periodic external fields of arbitrary strength or frequency.

Time-dependent magnetotransport in a driven graphene spin valve

Based on the time-dependent nonequilibrium Green's function method we investigate theoretically the time and spin-dependent transport through a graphene layer upon the application of a static bias voltage to the electrodes and a time-alternating gate voltage to graphene. The electrodes are magnetic with arbitrary mutual orientations of their magnetizations. We find features in the current that are governed by an interplay of the strength of the alternating field and the Dirac point in graphene: The influence of a weak alternating field on the zero bias conductance is strongly suppressed by the zero density of state at the Dirac point. In contrast, for a strong amplitude of the alternating field the current is dominated by several resonant peaks, in particular a marked peak appears at zero bias. This subtle competition results in a transition of the tunnel magnetoresistance from a broad peak to a sharp dip at a zero bias voltage applied to the electrodes. The dip amplitude can be manipulated by tuning the ac field frequency.

Coupling optical and electrical gating for electronic readout of quantum dot dynamics

We explore the coherent transfer of electronic signatures from a strongly correlated, optically gated nanoscale quantum dot to a weakly interacting, electrically backgated microscale channel. In this unique side-coupled ``$T$'' geometry for transport, we predict a mechanism for detecting Rabi oscillations induced in the dot through quantum, rather than electrostatic means. This detection shows up directly in the dc conductance-voltage spectrum as a field-tunable split in the Fano lineshape arising due to interference between the dipole coupled dot states and the channel continuum. The split is further modified by the Coulomb interactions within the dot that influence the detuning of the Rabi oscillations. Furthermore, time resolving the signal we see clear beats when the Rabi frequencies approach the intrinsic Bohr frequencies in the dot. Capturing these coupled dynamics requires attention to memory effects and quantum interference in the channel as well as many-body effects in the dot. We accomplish this coupling by combining a Fock-space master equation for the dot dynamics with the phase-coherent, non-Markovian time-dependent nonequilibrium Green's function transport formalism in the channel through a properly evaluated self-energy and a Coulomb integral. The strength of the interactions can further be modulated using a backgate that controls the degree of hybridization and charge polarization at the transistor surface.

Time-dependent spintronic transport and current-induced spin transfer torque in magnetic tunnel junctions

The responses of the electrical current and the current-induced spin transfer torque (CISTT) to an ac bias in addition to a dc bias in a magnetic tunnel junction are investigated by means of the time-dependent nonequilibrium Green function technique. The time-averaged current (time-averaged CISTT) is formulated in the form of a summation of dc current (dc CISTT) multiplied by the product of Bessel functions with the energy levels shifted by $m\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0}.$ The tunneling current can be viewed to occur between the photonic sidebands of the two ferromagnets. The electrons can pass through the barrier easily under high frequencies but difficultly under low frequencies. The tunnel magnetoresistance almost does not vary with an ac field. It is found that the spin transfer torque, still being proportional to the electrical current under an ac bias, can be changed by varying frequency. Low frequencies could yield a rapid decrease of the spin transfer torque, while a large ac signal leads to a decrease of both the electrical current and the spin torque. If only an ac bias is present, the spin transfer torque is sharply enhanced at the particular amplitude and frequency of the ac bias. A nearly linear relation between such an amplitude and frequency is observed.