Nonequilibrium Green Function Approach Research Articles

Thermodynamic uncertainty relation for energy transport in a transient regime: A model study.

We investigate a transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production. We explore this relation in the context of energy transport in a bipartite setting for three exactly solvable toy model systems (two coupled harmonic oscillators, two coupled qubits, and a hybrid coupled oscillator-qubit system) and analyze the role played by the underlying statistics of the transport carriers in the TUR. Interestingly, for all these models, depending on the statistics, the TUR ratio can be expressed as a sum or a difference of a universal term which is always greater than or equal to 2 and a corresponding entropy production term. We find that the generalized version of the TUR, originating from the universal fluctuation symmetry, is always satisfied. However, interestingly, the specialized TUR, a tighter bound, is always satisfied for the coupled harmonic oscillator system obeying Bose-Einstein statistics. Whereas, for both the coupled qubit, obeying Fermi-like statistics, and the hybrid qubit-oscillator system with mixed Fermi-Bose statistics, violation of the tighter bound is observed in certain parameter regimes. We have provided conditions for such violations. We also provide a rigorous proof following the nonequilibrium Green's function approach that the tighter bound is always satisfied in the weak-coupling regime for generic bipartite systems.

Tunable conductance and spin filtering in twisted bilayer copper phthalocyanine molecular devices.

We investigate theoretically the quantum transport properties of a twisted bilayer copper phthalocyanine (CuPc) molecular device, in which the bottom-layer CuPc molecule is connected to V-shaped zigzag-edged graphene nanoribbon electrodes. Based on a non-equilibrium Green's function approach in combination with density-functional theory, we find that the twist angle effectively modulates the electron interaction between the bilayer CuPc molecules. HOMO (highest occupied molecular orbital)–LUMO (lowest unoccupied molecular orbital) gap, spin filtering efficiency (SFE) and spin-dependent conductance of the bilayer CuPc molecular device could be modulated by changing the twist angle. The conductance reaches its maximum when the twist angle θ is 0° while the largest SFE is achieved when θ = 60°. The twist angle-induced exotic transport phenomena can be well explained by analyzing the transmission spectra, molecular energy level spectra and scattering states of the twisted bilayer CuPc molecular device. The tunable conductance, HOMO–LUMO gap and spin filtering versus twist angle are helpful for predicting how a two-molecule system may behave with twist angle.

Current response of nonequilibrium steady states in the Landau-Zener problem: Nonequilibrium Green's function approach

The carrier generation in insulators subjected to strong electric fields is characterized by the Landau-Zener formula for the tunneling probability with a nonperturbative exponent. Despite its long history with diverse applications and extensions, study of nonequilibrium steady states and associated current response in the presence of the generated carriers has been mainly limited to numerical simulations so far. Here, we develop a framework to calculate the nonequilibrium Green's function of generic insulating systems under a DC electric field, in the presence of a fermionic reservoir. Using asymptotic expansion techniques, we derive a semi-quantitative formula for the Green's function with nonperturbative contribution. This formalism enables us to calculate dissipative current response of the nonequilibrium steady state, which turns out to be not simply characterized by the intraband current proportional to the tunneling probability. We also apply the present formalism to noncentrosymmetric insulators, and propose nonreciprocal charge and spin transport peculiar to tunneling electrons.

Modelling of InAs nanowire and MOSFET under phonon emission and absorption by using NEGF formalism

Applying the nonequilibrium Green's function (NEGF), we have compared the performance of InAs nanowire (NW) and its based superlattice MOSFET under optical phonon absorption and emission. Our results indicate fluctuations in the NW characteristics like density of states (DOS), scattering rate, mobility, effective transmission and current. We applied the NEGF approach to show fluctuations in the NW parameters as a function of the energy. Electron phonon interactions and background effect are also taken into account through scattering self-energies in the self-consistent born approximation. The energy dependence of these oscillations allows us to deduce a coupling between electrons and the phonons. This analysis opens the door for InAs NWs as nano electromechanical devices, superlattice MOSFET and particularly, as phonon detectors. • Semiconductor nanowire based devices and superlattice MOSFET have potential applications in many areas, such as optoelectronics, sensors, and particularly integrated logic circuits. • Identification of InAs nanowire (NW) and its based superlattice MOSFET have been done here. • A nonequilibrium green's function model has been developed here to explore NWs. • The mentioned nonequilibrium green's function can provide accurate and detailed device performances of NWs in the presence of electron phonon interactions.

Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium

We investigate out-of-equilibrium dynamics in an excitonic insulator (EI) with a finite momentum pairing perturbed by a laser-pulse excitation and a sudden coupling to fermionic baths. The transient dynamics of the excitonic order parameter is resolved using the full nonequilibrium Green's function approach and the generalized Kadanoff-Baym ansatz (GKBA) within the second-Born approximation. The comparison between the two approaches after a laser pulse excitation shows a good agreement in the weak and the intermediate photo-doping regime. In contrast, the laser-pulse dynamics resolved by the GKBA does not show a complete melting of the excitonic order after a strong excitation. Instead we observe persistent oscillations of the excitonic order parameter with a predominant frequency given by the renormalized equilibrium bandgap. This anomalous behavior can be overcome within the GKBA formalism by coupling to an external bath, which leads to a transition of the EI system towards the normal state. We analyze the long-time evolution of the system and distinguish decay timescales related to dephasing and thermalization.

Light Amplification without Inversion from Hybrid Quantum Dot–Resonator Circuit: Floquet Nonequilibrium Green's Function Approach

Herein, a new mechanism of steady‐state light amplification without inversion from a hybrid quantum dot circuit coupled to a single mode of electromagnetic resonator is theoretically investigated. Hybrid quantum dot circuit consists of a single‐level quantum dot which is connected weakly to one normal metal electrode and strongly to one superconducting electrode. Using the Floquet nonequilibrium Green's function technique, it is shown that the gain originates from the Andreev reflection processes at proper gate voltages when the bias voltage exceeds a certain threshold. Also, it is found that the inversionless light amplification is mediated by spin transitions between Andreev and Floquet–Andreev bound states in the superconducting energy gap.

Quantum Transport in a Silicon Nanowire FET Transistor: Hot Electrons and Local Power Dissipation.

A review and perspective is presented of the classical, semi-classical and fully quantum routes to the simulation of electro-thermal phenomena in ultra-scaled silicon nanowire field-effect transistors. It is shown that the physics of ultra-scaled devices requires at least a coupled electron quantum transport semi-classical heat equation model outlined here. The importance of the local density of states (LDOS) is discussed from classical to fully quantum versions. It is shown that the minimal quantum approach requires self-consistency with the Poisson equation and that the electronic LDOS must be determined within at least the self-consistent Born approximation. To bring in this description and to provide the energy resolved local carrier distributions it is necessary to adopt the non-equilibrium Green function (NEGF) formalism, briefly surveyed here. The NEGF approach describes quantum coherent and dissipative transport, Pauli exclusion and non-equilibrium conditions inside the device. There are two extremes of NEGF used in the community. The most fundamental is based on coupled equations for the Green functions electrons and phonons that are computed at the atomically resolved level within the nanowire channel and into the surrounding device structure using a tight binding Hamiltonian. It has the advantage of treating both the non-equilibrium heat flow within the electron and phonon systems even when the phonon energy distributions are not described by a temperature model. The disadvantage is the grand challenge level of computational complexity. The second approach, that we focus on here, is more useful for fast multiple simulations of devices important for TCAD (Technology Computer Aided Design). It retains the fundamental quantum transport model for the electrons but subsumes the description of the energy distribution of the local phonon sub-system statistics into a semi-classical Fourier heat equation that is sourced by the local heat dissipation from the electron system. It is shown that this self-consistent approach retains the salient features of the full-scale approach. For focus, we outline our electro-thermal simulations for a typical narrow Si nanowire gate all-around field-effect transistor. The self-consistent Born approximation is used to describe electron-phonon scattering as the source of heat dissipation to the lattice. We calculated the effect of the device self-heating on the current voltage characteristics. Our fast and simpler methodology closely reproduces the results of a more fundamental compute-intensive calculations in which the phonon system is treated on the same footing as the electron system. We computed the local power dissipation and “local lattice temperature” profiles. We compared the self-heating using hot electron heating and the Joule heating, i.e., assuming the electron system was in local equilibrium with the potential. Our simulations show that at low bias the source region of the device has a tendency to cool down for the case of the hot electron heating but not for the case of Joule heating. Our methodology opens the possibility of studying thermoelectricity at nano-scales in an accurate and computationally efficient way. At nano-scales, coherence and hot electrons play a major role. It was found that the overall behaviour of the electron system is dominated by the local density of states and the scattering rate. Electrons leaving the simulated drain region were found to be far from equilibrium.

Time-dependent thermoelectric transport in mesoscopic systems under a quantum quench

We investigate the transient behavior of the quantum transport in mesoscopic systems under a quantum quench within the Caroli scheme. Using the nonequilibrium Green's function approach, an exact solution of the transient electric current, energy current, and their fluctuations in the presence of both external bias and temperature gradient are presented that goes beyond the wide-band limit. The exact solution of the time-dependent Seebeck coefficient in the linear response regime is also obtained. This formalism is applied to study the transient behavior of a single-level quantum dot with Lorentzian linewidth induced by the temperature gradient. The damped oscillatory behavior is found in the transient electric and energy currents, as well as their fluctuations. The oscillation frequency of electric and energy currents increases with the increasing energy level of quantum dot and the decay rate of oscillation decreases as the bandwidth increases. A significantly enhanced Seebeck coefficient is generated in the transient regime. We find the maximum value of the time-dependent Seebeck coefficient can be enhanced by increasing the energy level of the quantum dot and the reference temperature of leads.

Tailoring optoelectronic properties of monolayer transition metal dichalcogenide through alloying

We conducted a methodical investigation of the electronic and optical properties of monolayer transition metal dichalcogenides by employing first principles calculation. We have calculated the lattice constants, bond lengths for MoSe2 and MoTe2 and their alloy Mo (Se0.5Te0.5)2. A details analysis of the band structures indicates that spin—orbit coupling plays an important role making the band gaps to smaller and enhance in electron effective masses. Optical properties acting as imaginary and real parts of dielectric function, have been discussed in consideration of alloying effect. Furthermore, the transport properties of Mo(Se0.5Te0.5)2 alloy monolayer were calculated using the schema of density functional theory mingled to nonequilibrium Green's function approach. We reported the transmission for zero bias and discussed its features in light of the projected local densities of states. The device I-V curves were also reported by discussing the effect of the voltage applied across the metal dichalcogenides electrical devices and the current flowing through it.

Electron-Transport Characteristics through Aluminum Oxide (100) and (012) in a Metal-Insulator-Metal Junction System: Density Functional Theory-Nonequilibrium Green Function Approach.

Al2O3 is commonly used in modern electronic devices because of its good mechanical properties and excellent electrical insulating property. Although fundamental understanding of the electron transport in Al2O3 is essential for its use in electronic device applications, a thorough investigation for the electron-transport mechanism has not been conducted on the structures of Al2O3, especially in nanometer-scale electronic device settings. In this work, electron transport via Al2O3 for two crystallographic facets, (100) and (012), in a metal–insulator–metal junction configuration is investigated using a density functional theory-based nonequilibrium Green function method. First, it is confirmed that the transmission function, T(E), decreases as a function of energy in (E – EF) < 0 regime, which is an intuitively expected trend. On the other hand, in the (E – EF) > 0 regime, Al2O3(100) and Al2O3(012) show their own characteristic behaviors of T(E), presenting that major peaks are shifted toward lower energy levels under a finite bias voltage. Second, the overall conductance decay rates under zero bias are similar regardless of the crystallographic orientation, so that the contact interface seemingly has only a minor contribution to the overall conductance. A noteworthy feature at the finite bias condition is that the electrical current drastically increases as a function of bias potential (>0.7 V) in Al2O3(012)-based junction compared with the Al2O3(100) counterpart. It is elucidated that such a difference is due to the well-developed eigenchannels for electron transport in the Al2O3(012)-based junction. Therefore, it is evidently demonstrated that at finite bias condition, the contact interface plays a key role in determining insulating properties of Al2O3–Pt junctions.

Thermal boundary resistance predictions with non-equilibrium Green's function and molecular dynamics simulations

The nonequilibrium Green's function (NEGF) method with Büttiker probe scattering self-energies is assessed by comparing its predictions for the thermal boundary resistance with molecular dynamics (MD) simulations. For simplicity, the interface of Si/heavy-Si is considered, where heavy-Si differs from Si only in the mass value. With Büttiker probe scattering parameters tuned against MD in homogeneous Si, the NEGF-predicted thermal boundary resistance quantitatively agrees with MD for wide mass ratios. Artificial resistances that the unaltered Landauer approach yields at virtual interfaces in homogeneous systems are absent in the present NEGF approach. Spectral information results from NEGF in its natural representation without further transformations. The spectral results show that the scattering between different phonon modes plays a crucial role in thermal transport across interfaces. Büttiker probes provide an efficient and reliable way to include anharmonicity in phonon related NEGF. NEGF including the Büttiker probes can reliably predict phonon transport across interfaces and at finite temperatures.

Efficient computation of the second-Born self-energy using tensor-contraction operations.

In the nonequilibrium Green's function approach, the approximation of the correlation self-energy at the second-Born level is of particular interest, since it allows for a maximal speed-up in computational scaling when used together with the generalized Kadanoff-Baym ansatz for the Green's function. The present day numerical time-propagation algorithms for the Green's function are able to tackle first principles simulations of atoms and molecules, but they are limited to relatively small systems due to unfavorable scaling of self-energy diagrams with respect to the basis size. We propose an efficient computation of the self-energy diagrams by using tensor-contraction operations to transform the internal summations into functions of external low-level linear algebra libraries. We discuss the achieved computational speed-up in transient electron dynamics in selected molecular systems.

Design of graphene waveguides: Effect of edge orientation and waveguide configuration

Electron transport in a graphene quantum well can be analogous to photon transmission in an optical fiber. In this work, we present a detailed theoretical analysis to study the transport characteristics of graphene waveguides under the influence of different edge orientations. Non-equilibrium Green's function approach in combination with tight-binding Hamiltonian has been utilized to investigate the conductance properties of straight armchair and zigzag oriented graphene waveguides. Conductance plateaus at integer steps of $4e^2/h$ have been observed in both orientations while the zigzag oriented waveguides present a wider first quantized plateau compared to that in the armchair oriented ones. Using various geometric and physical parameters, including side-barrier and waveguide width, and the metallic properties of terminals, we investigate the conductance profile of waveguides. In addition to the observation of valley-symmetry in both edge orientations, this article explores the critical influence of drain contacts on waveguide conductance. Furthermore, we extended our transport study to three different highly bent waveguide configurations, such as U-shape, L-shape and split-shape waveguides, in order to explore their applications in graphene-based ballistic integrated circuit devices. In the end, we also calculated the conductance of larger graphene waveguides using the scalable tight-binding model, in order to compare the results obtained from the original model.

Energy Bandpass Filtering in Superlattice Phase Change Memories

We propose energy bandpass filtering employed using the idea of anti-reflection heterostructures as a means to reduce the energy requirements of a superlattice phase change memory based on GeTe and Sb$_{2}$Te$_{3}$ heterostructures. Different configurations of GeTe/Sb$_{2}$Te$_{3}$ superlattices are studied using the non-equilibrium Green's function approach. Our electronic transport simulations calculate the coupling parameter for the high resistance covalent state, to $97 \%$ that of the stable low resistance resonant state, maintaining the ON/OFF ratio of 100 for a reliable read operation. By examining various configurations of the superlattice structures we conclude that the inclusion of anti-reflection units on both sides of the superlattice increases the overall ON/OFF ratio by an order of magnitude which can further help in scaling down of the memory device. It is also observed that the device with such anti-reflection units exhibits 32$\%$ lesser RESET voltage than the most common PCM superlattice configurations and 27$\%$ in the presence of elastic dephasing. Moreover, we also find that the ON/OFF ratios in these devices are also resilient to the variations in the periodicity of the superlattice.

First-Principles Nonequilibrium Green's Function Approach to Ultrafast Charge Migration in Glycine.

We investigate the photoinduced ultrafast charge migration phenomenon in the glycine molecule using a recently proposed nonequilibrium Green's functions (NEGF) approach. We first consider the dynamics resulting from the sudden removal of an electron in the valence shells, finding a satisfactory agreement with available data. Then we explicitly simulate the laser-induced photoionization process and study the evolution of the system after the pulse. We disentangle polarization and correlation effects in the electron dynamics and assign the main frequencies to specific elements of the reduced one-particle density matrix. We show that electronic correlations renormalize the bare frequencies, redistribute the spectral weights, and give rise to new spectral features.

Spin induced inverter circuit with trinuclear chromium complexes

Density functional theory is used in conjunction with the non-equilibrium Green's functions approach to explore the spin polarized charge transport properties of homo-nuclear tri‑chromium and hetero-nuclear chromium‑ruthenium metal-string complexes. The metal strings comprise Cr-Cr-Cr, Cr-Cr-Ru, Cr-Ru-Cr, and Cr-Ru-Ru metal centers that are sandwiched between two Au (111) nano-electrodes. As deduced from the results, the Cr-Cr-Cr metal-string junctions could potentially be exploited in designing an inverter logic circuit to transfer the data at nanoscale. Considerably It also turns out that, among these single molecular junctions, Cr-Cr-Ru and Cr-Ru-Ru exhibit significant spin-up filtering with about 100% efficiency. More importantly, the Cr-Ru-Ru metal string complex demonstrates the negative differential resistance (NDR) effects in addition to its spin filtering properties. To analyze these phenomena, we examine the respective transmission spectra along with the potential drop across all the four metal-string junctions.

A computationally efficient hybrid approach based on artificial neural networks and the wavelet transform for quantum simulations of graphene nanoribbon FETs

Numerical modeling of graphene nanoribbon field-effect transistors (GNRFETs) using quantum-mechanical approaches is often associated with a heavy computational burden, indicating the urgent need for new methods to resolve this issue. A computationally efficient hybrid approach for quantum simulations of ballistic GNRFETs is developed herein. The proposed simulation method is based on solving the two-dimensional (2D) Poisson equation using both wavelet-based adaptive meshing and wavelet-based matrix compression techniques, self-consistently, with well-trained neural network models that imitate the mode-space (MS) nonequilibrium Green’s function (NEGF) solver in generating the charge density. The results obtained by applying the hybrid approach show good agreement with NEGF simulations. Numerical experiments reveal that the developed simulation method can offer a speed-up of about one order of magnitude over the conventional MS NEGF approach. The encouraging results obtained in this work indicate that the developed numerical model is particularly appropriate for incorporation into nanoelectronic device simulators to investigate future GNRFET-based circuits.

Steering Magnetic Skyrmions with Currents: A Nonequilibrium Green's Functions Approach

Magnetic skyrmions, topologically protected vortex‐like configurations in spin textures, are of wide conceptual and practical appeal, notably in relation to the making of so‐called race‐track memory devices. Skyrmions can be created, steered, and destroyed with magnetic fields and/or (spin) currents. Here the authors focus on the latter mechanism, analyzed via a microscopic treatment of the skyrmion–current interaction. The system considered is an isolated skyrmion in a square‐lattice cluster, interacting with electron spins in a current‐carrying quantum wire. For the theoretical description, a quantum formulation of spin‐dependent currents via nonequilibrium Green's functions (NEGF) within the generalized Kadanoff–Baym ansatz (GKBA) is employed. This is combined with a treatment of skyrmions based on classical localized spins, with the skyrmion motion described via Ehrenfest dynamics. With the mixed quantum–classical scheme, the authors assess how time‐dependent currents can affect the skyrmion dynamics, and how this in turn depends on electron–electron and spin–orbit interactions in the wire. This study shows the usefulness of a quantum–classical treatment of skyrmion steering via currents, as a way for example to validate/extract an effective, classical‐only, description of skyrmion dynamics from a microscopic quantum modeling of the skyrmion–current interaction.

Ballistic transport in bent-shaped carbon nanotubes

We report theoretical investigations of ballistic quantum transport properties of smoothly bent semiconducting single-walled carbon nanotubes (SWCNTs). The SWCNT is doped into NxN and PxP forms where N and P stand for N-type and P-type doping, x takes N-type, P-type or intrinsic I-type. Our calculation is based on a state-of-the-art non-equilibrium Green's function approach combined with density functional theory. The smooth bent induces a small electron redistribution on the SWCNT arc, which leads to rich and major transport differences between the NxN and PxP tubes. Conductance G of NNN tubes does not change with the bending angle β, while G of PPP tubes decreases with it. G of NPN and PNP tubes increases with β, while that of the PNP tubes varies with it in an oscillatory manner. The bent induced transport phenomena can be well understood by analyzing the microscopic physics of the electronic density distribution and quantum interferences between scattering states which traverse different paths along the bent-shaped tubes. The predicted conductance versus bent angle is useful for estimating how a flexible system may behave when strained and/or bent.

Investigation of Effects of Diameter, Doping and Vacancy Defects on the Band Structure and Transport Properties of Silicon Nanowires for Potential Applications in Field-Effect Transistors

Silicon nanowires (SiNWs) with unique band structure and transport properties are considered potential candidates for future nanoelectronics devices such as field-effect transistors (FETs). We present a model of a SiNW-FET comprising $$\langle100\rangle$$ silicon atomic wires with a cylindrical-shaped metallic gate wrapped around the wires. For this purpose, we report on the energy band structure and density of states of SiNWs of diameters 5.93 A, 9.71 A and 13.55 A with $$\langle100\rangle$$ cleavage orientation by employing generalized gradient approximation and meta-generalized gradient approximation as well as the semi-empirical extended-Huckel model. Moreover, the transmission and transport properties of doped and undoped SiNWs of diameter 5.93 A with and without vacancy defects are explored using a non-equilibrium green function approach with self-consistent calculations. The corresponding I–V characteristics of the proposed cylindrical-shaped metallic-gate SiNW-FET under a specific gate voltage are presented. Our results show that the undoped SiNWs with vacancy defects on the surface are more suitable candidates for nanoelectronic device applications such as FETs in contrast to their counterparts with vacancies at the center.