Green Function Method Research Articles

Andreev reflection imaging and longitudinal shift of pseudospin-1 fermions in two-dimensional materials

In this work, the transverse magnetic focusing of pseudospin-1 fermions in two-dimensional materials with a superconducting contact is studied. The transmission coefficient and Andreev reflection coefficient from injector lead to collector lead are calculated based on the Landauer–Büttiker formula combined with the non-equilibrium Green's function method. The local state density diagrams of the electron and hole transmission in the center region are given, which provide a complete image of the ballistic electron–hole cyclotron orbits. Using these images, the positive longitudinal shift in Andreev reflection of the pseudospin-1 fermion can be obviously seen. Furthermore, it is found that the total offset is proportional to the number of Andreev reflection occurrence. This setup provides the possibility of detecting this shift experimentally.

Quantum Transport of Topological and Trivial Edge States in Sn‐Doped SbH Nanoribbons

Although the transport of topological edge states may be insensitive to impurities, impurities may induce the interedge scattering and backscattering in topological nanoribbons due to the finite size effect. It may be interesting to compare the transport of topological edge states with that of trivial edge states in nanoribbons. Here, the quantum transport of edge states in the Sn‐doped SbH nanoribbons using the density functional theory combined with nonequilibrium Green's function method is studied. Both topological and trivial edge states can be found in the zigzag SbH nanoribbons. The impurity generates a higher barrier near the doping position and leads to the scattering of the states. From calculations, the transmission of topological edge states can be smaller than that of trivial edge states due to the antiresonance behavior. Compared with topological edge states, the transport of trivial edge states is more sensitive to the impurity position. Besides, the edge impurity is more likely to induce scattering for both topological and trivial edge states than the central impurity in narrow SbH nanoribbons, since the transport channels are limited to the edges. This study may be helpful for understanding the transport of edge states in nanoribbons.

The evolution of penta-graphene thermoelectrics: External fields as a key enabler for High-Performance devices

The tight-binding model is used in this study to examine the electronic and thermal properties of penta-Graphene (PG). To analyze these properties, approaches including the Kubo formula, linear response theory, and Green's function method are applied. The obtained numerical results show that by introducing bias voltage U, external magnetic field Π, and electron doping μ, significant modifications in electrical conductivity, magnetic susceptibility, and thermoelectric properties including power factor PF(T), Seebeck coefficients S(T), and figure of merit ZT(T) are observed. The band structure and density of states (DOS) of PG structure can be significantly altered by applying a bias voltage or an external magnetic field. The wide band gap of PG exhibited a marked reduction with the application of these external fields, displaying greater sensitivity to Π compared to U. Thermal properties of PG, including electrical conductivity σ(T), exhibit a peak as a function of temperature, which its peak position depends on the external fields and μ. Below the peak, σ(T) increases significantly with increasing external fields and μ, due to the reduced band gap and increased number of excited charge carriers, respectively. σ(T) demonstrates greater sensitivity to μ compared to Π, and both parameters have a more pronounced effect than bias voltage U. The magnetic field and bias voltage shift the peak position of the power factor PF(T) in opposite directions. Through tuning of the external fields, which alters the electronic structure of PG, the ZT(T) can be enhanced and its rate of increase is more dependent on bias voltage than on magnetic field.

Spatiotemporal analysis of the runaway distribution function based on green function and regularization method

Runaway electrons (REs) in experimental advanced superconducting tokamak (EAST) typically have an energy level of tens of MeV. Synchrotron radiation images of REs contain a wealth of information, making it crucial to handle this data properly to uncover hidden features. We observed distinct synchrotron radiation images emitted by the REs at different time points throughout the discharges and the focus of our study was an Ohmic discharge characterized by an evident synchrotron pattern and weaker background radiation. This paper aims to verify the feasibility of utilizing the green function and regularization method to obtain the distribution function information of synchrotron radiation images on EAST. We reconstruct the radial density profile of the REs beam by assuming the monoenergetic nature of REs at different time points. We employ the Tikhonov regularization method for this purpose. The results indicate that the radial density profile of the REs beam follows a roughly Gaussian distribution. Moreover, the peak density of the REs beam shifts inward to the magnetic axis as time progresses, a behavior also observed in the experimental image. However, a good fit between the simulated and experimental images is not achieved for all time points. This discrepancy is likely due to the intervention of magnetic islands and the increased complexity of the distribution function in both radial and momentum spaces.

A Semi-Analytical Model for Studying the Transient Flow Behavior of Nonuniform-Width Fractures in a Three-Dimensional Domain

In the fracture propagation model, the assumption that hydraulic fractures with non-uniform widths have been successfully utilized to predict fracture propagation for decades. However, when one conducts post-fracture analysis, the hydraulic fracture is commonly simplified with a uniform width, which is contradictory to the real fracture models. One of the reasons for over-simplifying the fracture geometry in the post-fracture analysis can be ascribed to the fact that we are still lacking a model to characterize the pressure transient behavior of the nonuniform-width fractures which can induce three-dimensional flow around the fractures. In this work, on the basis of the Green function and Newman product method, the authors derived a semi-analytical model to account for the effect of non-uniform width distribution of the hydraulic fractures in a three-dimensional domain. In addition, the effect of the fracturing strategies on the well performance is investigated based on the developed semi-analytical model. The calculated results from the developed model show that the vertical flow in the vicinity of the fracture cannot be neglected if the fracture height is sufficiently small (e.g., hf = 10 m), and one can observe vertical elliptical flow and vertical pseudo-radial flow during the production. A nonuniform-width fracture can penetrate further into the reservoir with a lower injection rate (e.g., qi = 1.44 × 103 md). For the scenarios of high fracture permeability (i.e., kf = 1 × 105 md), a smaller fracture height, lower injection rate, and larger Young’s modulus can be more favorable for enhancing the well productivity. Compared to the influence of fracture height, the influences of injection rate and Young’s modulus on the well performance are less pronounced.

Study of the pressure transient behavior of directional wells considering the effect of non-uniform flux distribution

During the production, the fluid in the vicinity of the directional well enters the wellbore with different rates, leading to non-uniform flux distribution along the directional well. However, in all existing studies, it is oversimplified to a uniform flux distribution, which can result in inaccurate results for field applications. Therefore, this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution. Specifically, the direction well is discretized into a carefully chosen series of linear sources, such that the complex well trajectory can be captured and the non-uniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior. By using the finite difference method, we can obtain the numerical solutions of the transient flow within the wellbore. With the aid of Green's function method, we can obtain the analytical solutions of the transient flow from the matrix to the wellbore. The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow. Subsequently, on the basis of the proposed model, we conduct a comprehensive analysis of the pressure transient behavior of a directional well. The computation results show that the flux variation along the direction well has a significant effect on pressure responses. In addition, the directional well in an infinite reservoir may exhibit the following flow regimes: wellbore afterflow, transition flow, inclined radial flow, elliptical flow, horizontal linear flow, and horizontal radial flow. The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length. Furthermore, a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.

Variation of Cochran’s excitation frequency, capacittivity, and dissipation factor in rubidium dihydrogen phosphate crystal

Ferroelectric materials are getting great interest due to their large applications in modern electronics technology such as memory devices, pyroelectric detectors, modulators, and so on, rubidium dihydrogen phosphate (RDP) is a member of Potassium dihydrogen phosphate family of ferroelectric crystals. In De Gennes–Kobayashi pseudospin model few extra terms like phonon anharmonic terms, extra spin phonon interaction terms, four body interaction terms and electric field terms are included. Dielectric properties have been investigated. Statistical Green function method of Zubarev is employed to derive excitation frequency, capacittivity, and dissipation factor for RDP. Theoretical data are compared to experimental data of other workers for RDP.

Phase Transition Behavior in Antiferroelectric Copper Formate Tetrahydrate Crystal

Antiferroelectric properties of copper formate tetrahydrate (CFT) crystal having phase transition temperature at were investigated theoretically. CFT have a layer-type structure in which layers of are sandwiched between the layers of copper formate in the lattice plane. By considering modified two sublattice pseudospin lattice coupled mode model Hamiltonian and double-time temperature-dependent Green function method for antiferroelectric copper formate tetrahydrate (CFT) crystal, the phase transition properties of crystal have been studied. Expressions are derived for soft mode frequency, dielectric constant and loss tangent for considered crystal. Model values are fitted in the derived expressions and the dependence of the above properties on temperature have been calculated. Theoretically obtained results are compared with experimental data and show similarities between them. Dielectric constant as a function of temperature shows a behaviour of the first-order transition with a large discontinuity at the transition point. These properties can be employed in a wide range of applications including memory devices, solar cells, biosensors and photovoltaic devices.

Local resonance mechanism for enhancing the thermoelectric performance of PBCF-graphene nanoribbons

Phonon local resonance mechanism can effectively block phonon transport and thus reduce phonon thermal conductance. Inspired by this, we investigated the thermoelectric performance of Armchair-PBCF-graphene nanoribbons (A-PBCF-GNRs) and its branched structures by using non-equilibrium Green's function method. The results show that the thermoelectric performance of branched A-PBCF-GNRs can be significantly improved. Especially, the room-temperature ZT value of single branch A-PBCF-GNRs (SB-A-PBCF-GNRs) and double branch A-PBCF-GNRs (DB-A-PBCF-GNRs) can reach to 0.56 and 0.80, which is 1.5 and 2 times greater than that of A-PBCF-GNRs. Analysis shows that this is mainly attributed to the significant decrease in thermal conductance of branched A-PBCF-GNRs caused by the localized electronic and phonon states. Moreover, the mode resolved phonon transmission probabilities demonstrated that the local resonance mechanism of branched structure blocks the low-frequency acoustic phonon transmission. This work indicates the broad application prospects of the local resonance mechanism of branched structure in the thermoelectric field.

Conservation and breaking of pseudospin symmetry

Pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the lower component of the Dirac spinor. Here, we investigate the conservation and breaking of PSS in the single-nucleon resonant states, as an example, using Green's function method that provides a novel way to precisely describe not only the resonant energies and widths but also the spacial density distributions for both narrow and wide resonances. The PSS conservation and breaking are perfectly displayed in the evolution of resonant parameters and density distributions with the potential depth: In the PSS limit, i.e., when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign, PSS is exactly conserved with strictly the same energy and width between the PS partners as well as identical density distributions of the lower components. As the potential depth increases, the PSS is broken gradually with energy and width splittings and a phase shift in the density distributions.

Spin orbit induced anisotropic giant effective g factor and reduced effective mass in non-magnetic Sn1−xSrxTe mixed crystal

The binary and ternary telluride systems containing europium as one of the magnetic components exhibit a higher effective g factor and much lower effective mass due to strong spin-orbit and s/p-f hybridized interaction mediated by the dopant impurity. In this communication, we have exploited the same for a ternary mixed crystal Sn1−xSrxTe, with strontium as the non-magnetic counterpart of europium. We have derived a functional equation within the framework of effective mass representation, accounting for both spin-orbit interaction and the presence of a magnetic field. In the context of k→⋅π→ model, at first, two MW (Mitchell-Wallis) band edge states are diagonalized properly, and subsequently, the off-band edge states are treated using perturbation up to the k2 level. We derived the formulas for the effective g factor and effective mass by employing Green's function method, considering the presence of spin-orbit interaction, magnetic field, and Sr impurity and assuming band inversion model as applicable to Sn1−xSrxTe system. Finally, we conduct a comprehensive examination of the effective g factor, effective mass, and their respective anisotropies in Sn1−xSrxTe considering their dependence on carrier concentration and impurity levels at T=300K. We present extremely elevated effective g factor; g=2230, for n−Sn1−xSrxTe and g=2160, for p−Sn1−xSrxTe respectively with large anisotropies and correspondingly low effective mass mc,v=0.003m0 around x=0.014 in the concentration range 0.01×1019 cm−3 to 0.1×1019 cm−3. Irrespective of the unsaturated electronic shell of Sr, the existence of strong spin-orbit interaction refers to the strong coupling of band edge states across the band minima triggered by substitutional impurity. The occurrence of a substantial effective g factor and low effective mass is unique in such non-magnetic Sn1−xSrxTe mixed crystal ever reported.

Thermoelectric enhancement of a parallel double quantum dot system connecting to Luttinger liquid leads

In this work, we study the thermoelectric properties of the parallel-coupled double quantum dot connected to Luttinger liquid (LL) leads. By applying nonequilibrium Green's function methods, the expressions of the electron current, heat currents, and transport coefficients are derived. We mainly focus on the effect of intralead Coulomb interaction and the spatial asymmetry of the system. Various causes for the enhancement of the thermoelectric efficiency are investigated. We find that Coulomb interactions in the LL not only enhance quantum interference but also considerably enhance thermoelectric effects. For moderately strong intralead interaction, the figure of merit can be considerably high and reach over 60 in the case of weakly coupled to LL leads and detuning of the energy levels, while in the case of strongly coupled to LL leads and the two aligned levels, the figure of merit approaches 8. The quantum interference induced by the Coulomb interaction yields a very high thermoelectric efficiency when the intralead interaction is very strong. These results may provide a design rule for the development of high-efficiency thermoelectric devices and facilitate optimization of device performance.

Ultrahigh spin filter efficiency and large spin Seebeck polarization of binuclear manganese phthalocyanine molecular junctions on nickel electrodes

In this paper, we investigated the spin transport properties of binuclear manganese phthalocyanine (Mn2Pc2) spintronic devices sandwiched between two nickel electrodes using the non-equilibrium Green's function method in combination with density functional theory. Based on the calculation results, the Mn2Pc2 device exhibited excellent spin-filtering capabilities, demonstrating an exceptionally high spin filter efficiency (SFE). Irrespective of the parallel or antiparallel orientation of magnetization in the electrodes, we observed that when both manganese atoms were in a spin-up state, the SFE of spin-resolved currents under finite bias and the thermoelectric currents induced by temperature gradients at fixed temperatures were both close to 100%. The large spin Seebeck polarization of the Mn2Pc2 device was also obtained at low reference temperatures. This study explores the potential for developing multifunctional spintronic single-molecule devices using Ni−Mn2Pc2.

Non-Markovian master equation for quantum transport of fermionic carriers.

We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix in a closed form in both Markov and Born approximations. In the Markov approximation the master equation is solved analytically, whereas in the Born approximation the problem is reduced to an algebraic equation for the single particle density matrix in the Redfield form. The non-Markovian equation is shown to lead to resonant transport similar to Landauer's conductance. It is shown that in the deep non-Markovian regime the transport current can be matched with that obtained by the non-equilibrium Green's function method.

Studying the Adsorption of Gas Molecules and Defects on Modulating the Electronic Transport Characteristics of Monolayer Penta-BN2-Based Devices.

Two-dimensional atomic layer materials, as an important part of the post-Moore era, have recently become an ideal choice for the preparation of high-efficiency, low-power, and miniaturized gas sensors. In this work, our study utilized density functional theory and the nonequilibrium Green's function method to investigate the electronic properties of the pentagonal BN2 (P-BN2) monolayer, as well as its gas-sensing properties for organic and inorganic gases. We also investigated how defects affect the quantum transport properties of the P-BN2-based device. Our findings demonstrate that the CO, H2S, NH3, SO2, C2H5OH, C3H6OH, CH3OH, and CH4 undergo physisorption on the P-BN2 monolayer, while NO, NO2, C2H2, C2H4, and HCHO undergo chemisorption. Then, we analyzed the impact of gas molecules chemisorbed on the P-BN2 monolayer on the electronic transport properties of the P-BN2-based gas sensor. When these five gas molecules are adsorbed, the current of the P-BN2-based gas sensor is greatly reduced. In addition, the effect of defects on the quantum transport properties of the P-BN2-based device is investigated. The results indicate that defects of N, B, and BN atoms lead to a decrease in the current of P-BN2-based nanodevices. Moreover, both the adsorption of gas molecules and the formation of vacancy defects leading to a decrease in device current can be revealed by the local device density of states near the zero-bias Fermi level, elucidating their microscopic mechanisms. Finally, gas molecules can also cause a decrease in the current of defect systems. These theoretical studies are of great significance for exploring two-dimensional atomic layer materials as high-efficiency gas sensors.

Robust fast direct integral equation solver for three-dimensional doubly periodic scattering problems with a large number of layers

Frequency-domain wave scattering problems that arise in acoustics and electromagnetism can be often described by the Helmholtz equation. This work presents a boundary integral equation method for the Helmholtz equation in 3-D multilayered media with many doubly periodic smooth layers. Compared with conventional quasi-periodic Green's function method, the new method is robust at all scattering parameters. A periodizing scheme is used to decompose the solution into near- and far-field contributions. The near-field contribution uses the free-space Green's function in an integral equation on the interface in the unit cell and its immediate eight neighbors; the far-field contribution uses proxy point sources that enclose the unit cell. A specialized high-order quadrature is developed to discretize the underlying surface integral operators to keep the number of unknowns per layer small. We achieve overall linear computational complexity in the number of layers by reducing the linear system into block tridiagonal form and then solving the system directly via block LU decomposition. The new solver is capable of handling a 100-interface structure with 961.3k unknowns to 10−5 accuracy in less than 2 hours on a desktop workstation.

Effects of long‐range dispersive interaction on the electron transport in short single strands of guanine bases

AbstractWe study the effects of the long‐range dispersive interaction on the electron transport in short single strands of guanine bases (G)s employing the density functional theory combined with non‐equilibrium Green's function method. Effects of contacting position are considered by connecting atomic gold chain electrodes on different positions to adapt to possible realistic measurements. The dispersive interaction can modify the stacking structure and enhance the helicity of the molecules. The corresponding change in the electronic structure may result in much‐increased conductance and the rectification effect. The dispersive interaction may also be the key to the realization of first‐principles simulation of some systems.

Controllable Nernst and Seebeck effects in graphene with O-shaped Kekulé structure

The Nernst and Seebeck effects in graphene with uniform Kekulé lattice distortion have been studied using the tight-binding model combined with the nonequilibrium Green's function method. Numerical results of this work showed that due to the electron–hole symmetry, the Nernst coefficient is an even function of the Fermi energy, while the Seebeck coefficient is an odd function regardless of the magnetic field. The Nernst and Seebeck coefficients show peaks when the Fermi energy crosses the Landau levels at high magnetic fields or crosses the transverse subbands at the zero magnetic fields. The peak height can be very large when the Fermi energy approaches the Dirac point, the Seebeck coefficient can reach about 0.78 mV/K, and the Nernst coefficient can reach about 0.95 mV/K at the corresponding hopping energy modification parameter δ=0.03 and T=0.009t/kB≈288 K. When δ=0.08 and T=0.024t/kB≈766 K, the Seebeck coefficient (or Nernst coefficient) is still up to about 0.78 mV/K (or 0.95 mV/K). This suggests that tunable Seebeck and Nernst coefficients can be achieved because the bandgap is a function of the corresponding hopping energy modification parameter δ. Experimentally, δ can be modulated by changing the type and amount of atoms adsorbed on graphene. In strong magnetic fields, the Nernst coefficient does not depend on the chirality of the nanoribbon.

Interacting topological magnons in a checkerboard ferromagnet

This work is devoted to studying the magnon–magnon interaction effect in a two-dimensional checkerboard ferromagnet with the Dzyaloshinskii–Moriya interaction. Using a first-order Green function method, we analyze the influence of magnon–magnon interaction on the magnon band topology. We find that Chern numbers of two renormalized magnon bands are different above and below the critical temperature, which means that the magnon band gap-closing phenomenon is an indicator for one topological phase transition of the checkerboard ferromagnet. Our results show that the checkerboard ferromagnet possesses two topological phases, and its topological phase can be controlled either via the temperature or the applied magnetic field due to magnon–magnon interactions. Interestingly, it is found that the topological phase transition can occur twice with the increase in the temperature, which is different from the results of the honeycomb ferromagnet.

Chirality-dependent spin transport and spin Seebeck effect in the spiral spin chains

The observation of spin Seebeck effect has triggered intense research in the spintronics. Especially, it is considered to be one alternative method to generate pure spin current in magnetic materials. Here, the spin Seebeck coefficient and the spin figure of merit are calculated by using Green's function method in the spiral spin chain with Dzyaloshinskii–Moriya interaction (DMI). The Zeeman-like effect and the similarity between the chirality and the spin in the spiral spin chain are revealed according to the dispersion relation. In addition, we find that the spin Seebeck coefficient and the spin figure of merit show peaks around the magnon spin transmission channel. In the absence of external magnetic field, the spin Seebeck peaks for opposite chirality are degenerated. However, the spin Seebeck peaks are chirality-dependent in the presence of magnetic field, and the spin Seebeck peaks with opposite chirality locate at different chemical potentials, leading to the energy difference between the spin Seebeck peaks with opposite chirality. Furthermore, the energy difference is determined by the magnetic field and the DMI, and the energy difference becomes larger for stronger DMI or higher magnetic field.