Green Function Technique Research Articles

A Layered-Shell Model of Anisotropic Composites: Extension of the Milgrom and Shtrikman Model

In this work, the extension of the Milgrom and Shtrikman model to anisotropic composite materials containing n-layered hollow ellipsoidal inclusions, is presented. The effective properties of such materials are determined using the Green function techniques and interfacial operators. Here, the basic unit of the microstructure is a hollow system of contacting concentric ellipsoidal shells, each of which is made of one of the components. Space is packed with such units of different sizes, but the same proportions; the cavity within each such shell system is then packed with similar systems and this continues in an infinite nesting sequence. In the final configuration, the effective properties are inside and outside the basic unit of layered shells (n+1). For n=2 and in the case of isotropic material, it is shown that the effective compressibility covers all ranges of the Hashin-Strikman bounds.

Investigation on the transmission of Love waves due to an impulsive line source in a heterogeneous double porous rock structure.

The region around the reservoir sometimes encounters the seismic response of ground. The phenomena of Love waves propagation also caused by seismic activity which can further significantly influenced by an impulsive line source present in the rock structures of ground. The current study elucidates the propagation behavior of Love waves induced by an impulsive line source within the anisotropic layered heterogeneous double porous rock structures commonly found in proximity to the reservoir areas. The expression of the dispersion relation for the Love waves propagation due to an impulsive line source has been derived by using the Fourier transformation and Green's function technique. The above-mentioned rock composite structure is consisted of two different portions: upper transversely isotropic double porous (TIDP) layer medium and lower heterogeneous isotropic double porous half-space (IDP) medium. In the aforesaid half-space medium, both types of heterogeneities viz. linear and quadratic have been considered. The impacts of heterogeneity parameters associated with the lower heterogeneous IDP half-space, porosity parameter (corresponds to both upper TIDP layer and lower IDP half-space) and anisotropic parameter of TIDP layer on Love waves phase velocity have also been studied. Some special outlines have also been depicted graphically.

Impact of valley degeneracy on the thermoelectric properties of zig-zag graphene nanoribbons with staggered sublattice potentials and transverse electric fields.

This study investigates the band inversion of flat bands in zig-zag graphene nanoribbons (ZGNRs) using a tight-binding model. The band inversion results from symmetry breaking in the transverse direction, achievable through deposition on specific substrates such as separated silicon carbide or hexagonal boron nitride sheets. Upon band inversion, ZGNRs exhibit electronic structures characterized by valley degeneracy and band gap properties, which can be modulated by transverse electric fields. To explore the impact of this level degeneracy on thermoelectric properties, we employ Green's function techniques to calculate thermoelectric quantities in ZGNR segments with staggered sublattice potentials and transverse electric fields. Two carrier transport scenarios are considered: the chemical potential is positioned above and below the highest occupied molecular orbital. We analyze thermionic-assisted transport (TAT) and direct ballistic transport (DBT). Level degeneracy enhances the electric power factors of ZGNRs by increasing electrical conductance, while the Seebeck coefficient remains robust in the TAT scenario. Conversely, in DBT, the enhancement of the power factor primarily stems from improvements in the Seebeck coefficient at elevated temperatures.

Propagation of bending waves along the edge of a point-loaded piezoelectric plate on elastic foundation

An investigation on the propagation of bending waves along the edge of a piezoelectric thin plate resting on an elastic foundation (cf. Pasternak foundation) and under the action of a point-load is carried out in this paper. The displacement field of the plate is based on the classical plate theory. The Kelvin-Voigt type viscoelastic model is used to examine the viscous effect on the characteristics of the bending wave. The Moore-Gibson-Thompson (MGT) thermoelastic equation is solved for an external time variant harmonic heat source at the upper surface of the plate. The piezoelectric potential is obtained for an electrode-covered upper surface and an electrically shorted lower surface. The displacements of the propagating bending wave along the edge are examined under a time-harmonic point-load acting near the vicinity of the free edge of the plate. The well-known Green function technique and Fourier transform method are implemented to generate an analytical solution for the non-homogeneous boundary value problem. The examination of the derived explicit form of the dispersion relationship and the displacements of the bending edge wave under external loading are discussed and presented both analytically and graphically, and the results are summarized.

Phase transition investigation of ferroelectric and dielectric properties of (NH 2 CH 2 COOH)3 H2SO4 crystal using green function method and two sublattice PLCM model Hamiltonian

The Greens function technique and extended two sublattice pseudospin lattice coupled-mode (PLCM) model Hamiltonian have been applied to study the phase transition mechanism in (NH2CH2COOH)3H2SO4 compound. The two sublattice PLCM model Hamiltonian is modified by considering anharmonic phonon interactions, extra spin-lattice interactions, and an external applied electric field term. By using the double-time thermal-dependent Green function technique, the theoretical equations for the total shift, total width, normal mode frequency, transition temperature, relative permittivity, dielectric tangent loss, acoustic attenuation and spontaneous polarization are derived. By fitting the distinct model parameters in the theoretical equations, we calculated the temperature dependence of normal mode frequency, relative permittivity, tangent loss, acoustic attenuation and spontaneous polarization. The numerically obtained results are hold well and correlated with experimental data.

Multiferroic and Phonon Properties of the Double Perovskite Pr2FeAlO6.

With the help of a microscopic model and Green's function technique, we studied the multiferroic and phonon properties of the recently reported new multiferroic Pr2FeAlO6 (PFAO) compound, which belongs to the double perovskite A2BB'O6 family. The magnetization decreases with the increase in temperature and disappears at the ferromagnetic Curie temperature TCFM. The polarization increases with the application of an external magnetic field, indicating strong magnetoelectric coupling and confirming the multiferroic behavior of PFAO. In the curves of dependence of the phonon energy and their damping with respect to temperature, a kink is observed at TCFM. This is due to the strong anharmonic spin-phonon interactions, which play a crucial role below TCFM and are frequently observed in other double perovskite compounds. Above TCFM, only anharmonic phonon-phonon coupling remains. The phonon mode is controlled by an external magnetic field.

Spin-wave resonance frequency and quantum fluctuation of the (anti)ferri-(anti)ferrimagnetic double-layer superlattice

The Hamiltonian of a four-sublattice simple cubic superlattice was solved by applying the linear spin-wave theory and the retarded Green's function technique. This study focused on the spin-wave resonance frequency, energy gap, sublattice magnetization, and quantum fluctuations of the system. The results show that the spin quantum number, interlayer (intralayer) exchange couplings, and intralayer anisotropy have a significant influence. In the ground state, the magnetizations of the sublattices are smaller than their spin quantum numbers, indicating the existence of quantum zero-point vibrations in the (anti)ferrimagnetic-(anti)ferrimagnetic bilayer system.

Resonant tunneling via the corner states in the double-barrier-modulated second-order topological insulator

In this work, we use the Green's function technique and investigate transport properties of the electronic states in the two-dimensional (2D) second-order topological insulator (TI). We calculated the bulk, edge, and corner states corresponding respectively to the infinite plane, one-dimensional nanoribbon, and the square flake geometries of the 2D second-order TI. Existence of the corner states in the square flake is confirmed. In this approach, we considered tunneling via the localized corner states in the double-barrier-modulated 2D second-order TI. Sharp peaks are found in the transmission probability and conductance incurred by the corner states lying within the surrounding energy gap. The relation between transmission peaks and the corner states is confirmed by their energy correspondence. The extremely discrete and sharp resonance might lend insight to experimental observation of the corner states in the 2D second-order TI.

Theoretical Investigation of Transport Properties of X-doped (X = Cl, P, N) Graphene Quantum Dots Layer Adsorbed with Ammonia Molecule Using Non-Equilibrium Green’s Function

This study investigates the various transport properties, including Density of States (DOS), Transmission Coefficient, Current-Voltage Characteristics (I-V), and HOMO-LUMO energy levels, of X-doped (X = Cl, P, N) graphene quantum dot (GQD) layers with adsorbed ammonia molecules using density functional theory and non-equilibrium Green's function techniques. Our findings revealed the profound influence of different doping and adsorption scenarios on the transport properties of GQD layers. Specifically, chlorine doping leads to notably stronger resonance peaks, resulting in enhanced conductivity of the GQD layer. This effect is less pronounced for P-doped and N-doped GQDs, which exhibit minimal changes in conductance capability. Importantly, we observed a prominent interaction between ammonia molecules and chlorine-doped GQD layers. The HOMO and LUMO energy levels exhibit double degeneracy, significantly impacting edge passivation and the finite dimensions of GQDs, consequently reducing the energy gap. As a result, chlorine-doped GQD layers with adsorbed ammonia molecules exhibit increased energy levels and stronger current characteristics compared to P-GQDs and N-GQDs. HOMO and LUMO are doubly degenerated which has a clear effect on edge passivation as well as the finite size of GQDs and reduces energy gap. Therefore, more energy level and stronger current is available for chlorine doped graphene quantum dots layer with adsorbed ammonia molecule than P-GQDs and N-GQDs. Our theoretical finding highlighted the significant features of edge passivation, doping effect and adsorption of ammonia molecule onto graphene quantum dots layer. Our theoretical analysis highlighted key features encompassing edge passivation, doping effects, and ammonia molecule adsorption on GQD layers. These insights not only develop our fundamental understanding of these systems but also hold promise for novel applications that harness their distinct electronic properties.

Theoretical Study of the Phonon Energy and Specific Heat of Ion-Doped LiCsSO4-Bulk and Nanoparticles.

Using a microscopic model, the temperature dependence of two phonon modes, ω0 = 32 cm-1 and 72 cm-1, and their damping of the ferroelastic LiCsSO4 compound, are calculated within Green's function technique. It is observed that the first mode increases whereas the second one decreases with increasing temperature T. This different behavior is explained with different sign of the anharmonic spin-phonon interaction constant. At the ferroelastic phase transition temperature TC, there is a kink in both modes due to the spin-phonon interaction. The phonon damping increases with T, and again shows an anomaly at TC. The contributions of the spin-phonon and phonon-phonon interactions are discussed. TC is reduced by decreasing the nanoparticle size, and can be enhanced by doping with K, Rb and NH4 ions at the Cs site. TC decreases by doping with Na, K or Rb on the Li site. The specific heat Cp also shows a kink at TC. Cp decreases with decreasing nanoparticle size and the peak disappears, whereas Cp increases with increasing K ion doping concentration.

Steric Effects on Single-Molecule Conductance in Flat-Lying Phenanthrene.

A previous combined experimental and theoretical study found that the position of anchoring groups on a phenanthrene (PHE) backbone played a large role in determining the single-molecule conductance of the PHE derivative. However, a consistent 0.1 G0 feature was found across all PHE derivatives. To understand this, the previously investigated PHE derivatives were placed flat on a simulated Au substrate with a scanning tunneling microscope (STM) tip over PHE and conductance was calculated using the non-equilibrium Green's function technique in conjunction with density functional theory (NEGF-DFT). The location of the tip was varied to find the most conductive and most energetically favorable arrangements, which did not coincide. Furthermore, the variation in conductance found in erect junctions was not present when PHE derivatives were lying flat, with all derivatives calculated to have conductance values around 0.1 G0.

Theory of electron spin resonance in scanning tunneling microscopy

Electron spin resonance (ESR) spectroscopy in scanning tunneling microscopy (STM) has enabled probing the electronic structure of single magnetic atoms and molecules on surfaces with unprecedented energy resolution, as well as demonstrating coherent manipulation of single spins. Despite this remarkable success, the field could still be greatly advanced by a more quantitative understanding of the ESR-STM physical mechanisms. Here, we present a theory of ESR-STM that quantitatively models not only the ESR signal itself, but also the full background tunneling current, from which the ESR signal is derived. Our theory is based on a combination of Green's function techniques to describe the electron tunneling and a quantum master equation for the dynamics of the spin system along with microwave radiation interacting with both the tunneling current and the magnetic system. We show that this theory is able to quantitatively reproduce the experimental results for a spin-1/2 system (TiH molecules on MgO) across many orders of magnitude in tunneling current, providing access to the relaxation and decoherence rates that govern the spin dynamics due to intrinsic mechanisms and to the applied bias voltage. More importantly, our work establishes that (i) sizable ESR signals, which are a measure of microwave-induced changes in the junction magnetoresistance, require surprisingly high tip spin polarizations, and (ii) the coupling of the magnetization dynamics to the microwave field gives rise to the asymmetric ESR spectra often observed in this spectroscopy. Additionally, our theory provides very specific predictions for the dependence of the relaxation and decoherence times on the bias voltage and the tip-sample distance. Finally, with the help of electromagnetic simulations, we find that the transitions in our ESR-STM experiments, in which the tunnel junction is irradiated by a nearby microwave antenna, can be driven by the ac magnetic field at the junction. Published by the American Physical Society 2024

Effect of static compression on near-field tsunami waves: Three-dimensional solution

An analytical solution of three-dimensional surface wave profiles due to arbitrary spatio-temporal disturbance of a circular ocean bottom in a compressible ocean is obtained by incorporating the influence of the static ocean background compression under the assumptions of linearized water wave theory. Time-domain simulations of the surface profile in three dimensions and the pressure distribution within the water column for a circular uniform rise and tilt are shown. The corresponding animation movies depict the temporal evolution of the surface profile and pressure field inside the water column eloquently, which was not shown in earlier literature. The impact of static compression is also discussed through the simulations. A novel analytical expression of the potential function for a generic tilted motion (rmcos(mθ),m∈Z) of the circular ocean floor is derived. An efficient numerical code is developed to find surface elevation and pressure distribution, implementing the inverse Fourier integral as matrix multiplication. Validation is performed for the specific case of a rising flat ocean floor, showing the oscillations due to acoustic-gravity modes. Initially, a simplified problem of a flat rising ocean bottom is solved using the eigenfunction matching method, which involves finding a particular solution for the nonhomogeneous ocean bottom condition and the solution for its homogeneous counterpart. Solutions are obtained using a newly developed inner product between the depth-dependent functions. Later, a Green function technique is used to incorporate the impact of the arbitrary spatio-temporal motion of the circular portion of the ocean bed. The solution obtained from the eigenfunction matching method is utilized to obtain the analytical form of Green’s function and, eventually, an expression of surface elevation and pressure distribution inside the ocean water column.

Theoretical Study of the Phonon and Electrical Conductivity Properties of Pure and Sr-Doped LaMnO3 Thin Films.

The film thickness, temperature, substrate and doping dependence of the phonon energy ω and damping γ, as well as the electrical conductivity, of pure and Sr-doped LaMnO3 thin films near the phase transition temperature TN are investigated using a microscopic model and the Green's function technique. Due to the strong spin-phonon interaction, there appears a kink at TN in the temperature dependence of ω(T) and γ(T). The softening and hardening of the ω = 495 cm-1 (A1g) and ω = 614 cm-1 (B2g) modes is explained by the different sign of the anharmonic spin-phonon interaction constant R. The damping increases with T for both cases because it is proportional to R2. ω decreases whereas γ increases with an increasing Sr concentration. This is due to the strain caused by the difference between the ionic radii of the La and Sr ions. The film thickness dependence is also considered. ω and γ increase strongly with the decreasing film thickness. The electrical conductivity is enhanced after the doping of the LMO thin films with Sr, which could be used for energy storage applications. The observed results are in good qualitative agreement with the experimental data.

Bandgap Energy of Ion‐Doped LaMnO3 Nanoparticles

Based on the s‐d model combined with Green's function technique, the magnetization and the bandgap energy of ion‐doped nanoparticles at La sites are calculated. Due to the change of the valency of Mn ions, from to , as well as the difference between the ionic radii of the doping and host ions, the exchange interaction is modified which allows a tuning of the magnetization and the bandgap energy. For nanoparticles, the bandgap is decreased by Ag and Ba doping, whereas it is increased by K and Sr doping. Macroscopic quantities such as the magnetization and the bandgap energy are directly related to microscopic parameters of the model. The simulations are qualitatively in good agreement with the experimental data.

Theoretical Study of Electric, Dielectric, and Optical Properties in Ion Doped Multiferroic SrFe12O19 Nanoparticles.

Electric, dielectric, and optical (band gap) properties of pure multiferroic as well as La- and Ni-doped SrFe12O19 (SFO) (at different sites) are investigated using a microscopic model and Green's function technique. The concentration dependence of the polarization P is considered for substitution of rare earths ions on the Sr sites. For a small La ion doping concentration, x = 0.1, La-doped SFO is ferroelectric, whereas for a larger doping concentration, for example x = 0.5, it is antiferroelectric. The real part of the dielectric constant ϵ increases with an increasing magnetic field h. ϵ decreases with an increasing frequency and La dopants. Therefore, La-doped SFO is suitable for microwave application with a low dielectric constant. The magnetic properties of pure SFO NPs are also studied. Ni doping at the Fe site of SFO leads to enhanced ferroelectric polarization and dielectric constant. The band gap decreases or increases by substitution of Ni or In ions on the Fe site, respectively. The results reveal that the tuned band gap of Ni-doped SFO makes it a crucial candidate for optoelectronic and solid oxide fuel cell applications.

Quantum mechanical-like approach with non-Hermitian effective Hamiltonians in spin-orbit coupled optical cavities

We present a comprehensive analytical model of resonant states in birefringent microcavities with permeable mirrors. We derive an effective, non-Hermitian photonic Hamiltonian describing cavity mode dispersion and modal lifetimes by applying the Green's function technique based on the Mittag-Leffler expansion with respect to the resonant states and the k·p perturbation theory known from semiconductor physics. Using this formalism we obtained results which can be interpreted as effective cavity mode spin-orbit coupling. We use this method to derive the two-mode Hamiltonian to describe the properties of light in the cavity, which significantly reduces the computational effort and properly captures the polarization of the eigenmodes. This is done by introducing the necessary corrections to the Hamiltonian matrix and modifying the basis modes resulting from the coupling with other optical modes present in the system. This simplified Hamiltonian allows us to determine the positions of exceptional points in momentum space. These points are connected by Fermi arcs and appear due to non-Hermiticity and PT symmetry. Published by the American Physical Society 2024

Electric, Dielectric, and Phonon Properties of Cu2OCl2

Investigating the multiferroic properties of , their temperature and magnetic‐field dependencies around the magnetic and ferroelectric phase transition temperatures and are analyzed using a microscopic model and Green's function technique. Near the Neel temperature , a kink in the specific heat and also in the phonon energy and damping due to strong anharmonic spin–phonon interaction is observed. The kink in disappears with increasing magnetic field h. The polarization shows also a small anomaly at and decreases with increasing magnetic field h. This behavior strongly suggests that exhibits multiferroic characteristics. A kink at can be seen in the real part of the dielectric constant , too. It should be noted that demonstrates a significant increase with increasing field strength h below , which is a pronounced magneto‐dielectric effect. These findings qualitatively agree with the experimental data.

Line Edge Roughness Effects on the Thermoelectric Properties of Armchair Black Phosphorene Nanoribbons

AbstractThis study delves into the thermoelectric properties of armchair black phosphorene nanoribbons while considering the presence of line edge roughness. Employing the tight‐binding method in conjunction with non‐equilibrium Green's function techniques and Landauer formulas, the impact of various parameters on thermoelectric performance is explored. These findings reveal that the electrical conductivity and, consequently, the power factor exhibits an increasing trend with expanding ribbon length and width. This behavior can be attributed to heightened collision rates, particularly in narrow ribbons, induced by line edge roughness as length increases. Remarkably, the Seebeck coefficient at the Fermi energy corresponding to the maximum power factor remains nearly constant across different widths, lengths, temperatures, and transport regimes. Furthermore, the thermoelectric figure of merit (ZT) demonstrates a positive correlation with both ribbon length and width. In narrow widths and lengths ≈1000 nm, the power factor and figure of merit exhibit an upward trend with ribbon width. However, with further increases in ribbon width, the influence of line edge roughness on thermal conductivity diminishes. Consequently, the figure of merit decreases due to the rise in thermal conductivity. Notably, the thermoelectric figure of merit is higher for short and narrow ribbons and long and wider ribbons.

Vibration spectra of DNA and RNA segments.

The dispersion curves and density of states are used to analyze the vibrational characteristics of DNA and RNA segments. This is done using a harmonic Hamiltonian and the Green's function technique. Two configurations of DNA and RNA, finite and cyclic, have been investigated and compared to their infinite counterparts. For the DNA molecule, three models, including a fishbone model, a ldder model, and a fishbone ladder model, have been employed, while the RNA molecule has been represented using a half fishbone model. To enhance the realism of DNA and RNA simulations, the unit cells within each infinite system as well as the length of the finite and cyclic cases are gradually enlarged. The connections between the sub-sites have been modeled using linear springs, where the stiffness of the vertical springs exhibits random variations throughout the length of the DNA and RNA models. Shorter DNA and RNA segments exhibit additional peaks in their density of states, resulting in more bands in dispersion curves. This indicates that as the number of building blocks grows in these segments, their curves resemble those of infinite systems. These findings have practical implications for studying the vibration characteristics of similar macro-systems.