Green Function Technique Research Articles

Nonlinear interaction effects in a three-mode cavity optomechanical system

We investigate the resonant enhancement of nonlinear interactions in a three-mode cavity optomechanical system with two mechanical oscillators. Using the Keldysh Green's function technique, we find that nonlinear effects on the cavity density of states can be greatly enhanced by the resonant interaction of two phononic polaritons, due to their small effective dissipation. In the large detuning limit and taking into account an upper bound on the achievable dressed coupling, the optimal point for probing the nonlinear effect is obtained, showing that such a three-mode system can exhibit significant nonlinear features also for relatively small values of $g/\ensuremath{\kappa}$.

Interaction of circular cavity and crack near anisotropic bi-material interface under SH-waves incidence

AbstractAn anisotropic bi-material interface with a circular hollow and a crack was used to explore the scattering of SH waves using complex variables and Green's function techniques. A horizontal interface in a bi-material media forms an elastic anisotropic half-space with a circular cavity and a linear crack, whereas the other half-space is an elastic isotropic half-space. The Green's function approach is used to derive the relevant Green's functions, which are then used in the “crack division” procedure to create a crack. During the joining of the two pieces, unknown anti-plane forces are applied to the horizontal surfaces to ensure the interface maintains its continuity criteria. For weakly singular integral equations, Fredholm integral equations are inferred and solved using the direct discrete technique. The simulation results were represented graphically to show how different parameters affect the influence of dynamic stress concentration factors around the cavity and dynamic stress intensity factors toward the crack tip. For example, a cavity's wave number and angle of incidence, as well as the distance between the cavity's center and its horizontal interface and its radius, are all elements that must be taken into consideration.

Effect of the hole concentration on the polaronic mobility for the strongly interacting electrons

The effective hopping of the polaron has been studied for different hole concentrations. Holstein-Hubbard model is used for the half-filled and less than half-filled cases. A series of canonical transformations are imposed on the generic Hamiltonian and considering the strongly interacting electrons, the transformed Hamiltonian has been reconstructed to an effective t-J model. Using the mean-filled Hartree-Fock approximation the electronic Hamiltonian has been solved with the Zuberev’s Green function technique. The effective polaronic transport is found to be strongly dependent on the electron and hole concentration of the system.

Local equilibrium charge and spin currents in two-dimensional topological systems

We study the equilibrium and nonequilibrium electronic transport properties of multiprobe topological systems using a combination of the Landauer-B\"uttiker approach and nonequilibrium Green's functions techniques. We obtain general expressions for both nonequilibrium and equilibrium local electronic currents that, by suitable projections, allow one to compute charge, spin, valley, and orbital currents. We show that external magnetic fields give rise to equilibrium charge currents in mesoscopic system and study the latter in the quantum Hall regime. Likewise, a spin-orbit interaction leads to local equilibrium spin currents, that we analyze in the quantum spin Hall regime. We show that an accurate theoretical assessment of the equilibrium currents is quite challenging and propose a two-measurement protocol that facilitates a comparison between experiment and theory.

First-principles calculations of spin-orbit torques in Mn2Au /heavy-metal bilayers

Using the nonequilibrium Green's function technique, we calculate spin-orbit torques in a ${\mathrm{Mn}}_{2}\mathrm{Au}$/heavy-metal bilayer, where the heavy metal (HM) is W or Pt. Spin-orbit coupling (SOC) in the bulk of ${\mathrm{Mn}}_{2}\mathrm{Au}$ generates a strong fieldlike torquance, which is parallel on the two sublattices and scales linearly with the conductivity, and a weaker dampinglike torquance that is antiparallel on the two sublattices. Interfaces with W or Pt generate parallel dampinglike torques of opposite signs that are similar in magnitude to those in ferromagnetic bilayers and similarly insensitive to disorder. The dampinglike torque efficiency depends strongly on the termination of the interface and on the presence of spin-orbit coupling in ${\mathrm{Mn}}_{2}\mathrm{Au}$, suggesting that the dampinglike torque is not due solely to the spin-Hall effect in the HM layer. Interfaces also induce antiparallel fieldlike and dampinglike torques that can penetrate deep into ${\mathrm{Mn}}_{2}\mathrm{Au}$.

Effect of interfacial intermixing on spin-orbit torque in Co/Pt bilayers

Using the first-principles non-equilibrium Green's function technique with supercell disorder averaging, we study the influence of interfacial intermixing on the spin-orbit torque in Co$\mid$Pt bilayers. Intermixing is modeled by inserting one or more monolayers of a disordered CoPt alloy between Co and Pt. Dampinglike torque is moderately enhanced by interfacial intermixing, while the fieldlike torque, which is small for abrupt interfaces, is strongly enhanced and becomes comparable to the dampinglike torque. The enhancement of the fieldlike torque is attributed to the interface between Co and the intermixed region. The planar Hall-like torque increases with intermixing but remains relatively small. The behavior of the torques is similar for bilayers with (111) and (001)-oriented interfaces. Strong dependence of the fieldlike torque on intermixing could provide a way to tune the fieldlike-to-dampinglike torque ratio by interface engineering.

Transport properties of the electronic states in the gate voltage-modulated skyrmion crystal

As a result of the Hund's coupling, the band structure of the conducting electrons in the skyrmion crystal (SkX) shares similar topological properties with that of graphene, such as its cone-like shape, nonzero band Chern number, edge states, and etc. In this work, we rigorously demonstrate that the Klein tunneling phenomena is also shared by these two. We use the Green's function technique and calculated the transmission probability of the electrons tunneling through an electrostatic barrier in the SkX expressed by the double exchange model. Numerical results of the SkX reproduced the Dirac model obtained by linear fitting the two-dimensional band structure of the SkX.

Application of Ion‐Doped Y3Fe5O12 Nanoparticles for Self‐Controlled Magnetic Hyperthermia

Herein, doped yttrium garnet (YIG) nanoparticles (NPs) ( Al, Ga, Sc are nonmagnetic ions) are studied, appropriate for self‐controlled magnetic hyperthermia (SCMH) for in vivo and in vitro applications. A microscopic model (modified Heisenberg Hamiltonian) and the Green's function technique are used to investigate the temperature, doping, and size dependence of magnetic phase transition, saturation magnetization, the coercivity, and the specific absorption rate coefficient to fulfill the conditions for magnetic hyperthermia. A set of mixed yttrium garnet magnetic NPs is found, which are suitable for applications in medicine for cancer therapy. There are two Sc‐doped YIG NPs which are the best candidates for SCMH with x = 1.08, d = 27.5 nm, and = 13.52 as well as x = 1.10, d = 29.7 nm, and = 15.44 for which the conditions for biocompatibility and maximization of are fulfilled simultaneously. Moreover, also Al‐ and Ga‐doped YIG NPs are found that can be applied for magnetic hyperthermia but with smaller effectivity.

Analytical solution of the convection-diffusion-reaction-source (CDRS) equation using Green's function technique

Convection-diffusion-reaction-source (CDRS) equation has been used to model a variety of transport phenomena. While several numerical methods for solving the CDRS equation exist, there is a relative lack of analytical solutions for the CDRS problem for an arbitrary source term. This work presents a Green's function based analytical solution to a one-dimensional, transient CDRS equation with an independent source/sink that can be a general function of space and time. Results compare well with past work as well as an independent numerical simulation. The model presented here is simple, computationally fast, and does not suffer from stability problems commonly encountered in numerical solutions of the CDRS equation. Furthermore, the model is used to solve a representative CDRS problem. The model presented here may help analyze transport problems in various engineering applications, such as drug delivery, heat transfer in reacting systems, and air pollution dispersion. The analytical solution may also serve as a building block for solving more complicated problems such as transport in a multilayer body, as well as for verifying numerical simulation tools.

The boundary integral equation for curved solid/liquid interfaces propagating into a binary liquid with convection

The boundary integral method is developed for unsteady solid/liquid interfaces propagating into undercooled binary liquids with convection. A single integrodifferential equation for the interface function is derived using the Green function technique. In the limiting cases, the obtained unsteady convective boundary integral equation transforms into a previously developed theory. This integral is simplified for the steady-state growth in arbitrary curvilinear coordinates when the solid/liquid interface is isothermal (isoconcentration). Finally, we evaluate the boundary integral for a binary melt with a forced flow and analyze how the melt undercooling depends on Péclet and Reynolds numbers.

Mott-Insulator to Peierls Insulator Transition in the Two-Dimensional Holstein-Hubbard Model

We propose a variational study of the two dimensional square lattice to study the phase transition from an antiferromagnetic SDW Mott insulator to the bipolaronic CDW Peierls insulator for the half-filled Holstein Hubbard model. The correlated system is dealt analytically in two different regimes according to the renormalized Coulomb correlation strength. Different unitary transformations are performed to obtain an effective electronic Hamiltonian which is solved by using the mean-field Hartree-Fock approximation for the weakly correlated electrons. For the strong interaction case, the Zuberev’s Green function technique is used to solve the effective t-J model at the mean field limit. The variations of the effective Hubbard hopping parameter and the effective Coulomb interaction strength for different electron–electron and electron–phonon interaction coefficients have been studied. We have found a transition from the Mott-insulator to a Peierls insulator analytically for the two dimensional Holstein Hubbard model.

Thermal Conductivity of BaxCa1-xTiO3

We have discussed the variation of thermal conductivity in the case of BaxCa1-xTiO3 ferroelectric perovskites using Silverman Hamiltonian in presence of defect and electric field and Green's Function Technique. The thermal conductivity decreases with the increasing electric field and defect. The results are consistent with previous experimental and theoretical results.

Electron passivation in CaF2 on calcium metal anodes.

Current electrolytes in calcium-ion batteries suffer from a lack of stability and degradation caused by reduction from the anode. The solid-electrolyte interphase (SEI) that forms on the anodes during operation stems the flow of electrons from the anode to the electrolyte. CaF2 is a common inorganic compound found in the SEI, and is derived from electrolyte salts such as Ca(PF6)2. CaF2 can exist in crystalline, polycrystalline, and amorphous phases in the SEI, and as recent work has shown, different phases of the same compound can have vastly different electronic conductivities. Using the non-equilibrium Green's function technique with density functional theory (NEGF-DFT), we find that amorphous phase systems enhance electron tunneling in thin CaF2 films by 1-2 orders of magnitude when compared to crystalline and polycrystalline CaF2 systems. Transport through several amorphous structures was considered showing that, despite their random structures, their conductance properties are similar. Through analysis of the decay constant β and the low-bias conductance of each system, we show that crystalline and polycrystalline CaF2 offer greater protection of the electrolyte than amorphous CaF2.

An iterative analytical model for aging analysis of Li-ion cells

Physics-based aging models are critical for understanding capacity degradation mechanisms in Li-ion batteries. This paper presents a technique for aging analysis of a Li-ion cell due to growth of the solid electrolyte interphase (SEI) layer driven by a solvent decomposition reaction at the electrode surface. The model employs an iterative technique based on the analytical solutions of the underlying conservation equations. The single-particle model describing Li-ion intercalation and de-intercalation processes is solved analytically using Green's function technique. The SEI formation problem is solved using the integral balance method. An iterative technique that combines these analytical solutions is shown to result in a converged result within a few iterations. The model is shown to agree well with results from past studies, as well as a numerical simulation. The capacity fade of Li-ion batteries is investigated under different operating conditions and different regimes, including both cycling and storage. The present model offers much faster computation time than numerical models for modeling the degradation of Li-ion cells. Further, the iterative technique described here may serve as a framework for semi-analytical solutions for other, more complicated problems. This work contributes towards improving the performance and reliability of electrochemical energy conversion and storage systems. • Developed an iterative technique for aging analysis of Li-ion cells. • Models capacity degradation due to cycling as well as calendar aging. • Results shown to agree well with past work and numerical simulations. • Results highlight key aspects of aging and capacity degradation in Li-ion cells.

Efficient current rectification in driven acenes.

We examine the current-voltage (I-V) characteristics of different polyacenes, such as anthracene, tetracene, pentacene, etc., under the influence of arbitrarily polarized light. The irradiation effect produces an anisotropy in the system and acenes may therefore be employed as molecular rectifiers. We find that the rectification efficiency can be more than 90% with a specific set of light parameters. The phase of rectification (positive or negative) can suitably be engineered by controlling the light conditions. The effect of light irradiation is incorporated through the Floquet-Bloch ansatz with the minimal coupling scheme. The transport properties are calculated using Green's function technique following the Landauer-Büttiker formalism. Given the promising rectification results, the present prescription may be useful in designing functional elements, employing several other single/complex molecular structures in digital circuit design with the possibility of immense applications.

Diffusion-controlled annihilation reactions in 2D and 3D nanostructures

An analytical consideration of bimolecular reactions in nanostructures is presented. As a mathematical model, the two-particle Green's function approach for the diffusion problem with the Neumann boundary condition is proposed. Also, the special cases, when the solutions can be reduced to the simpler one-particle Green's function, are analysed. Despite such diffusion equations are almost always analytically intractable, Green's function technique allows to build an analytical expression for the distance-dependent annihilation rate. The observed model can describe non-spin-selective annihilation reactions and spin-selective annihilation reactions such as triplet–triplet annihilation (TTA) of excitons or quenching of triplets by doublet centers. Based on this model, the distance-dependent annihilation rates were calculated for circular (2D system) and spherical (3D system) nanostructures. As illustrations of this method, we show that the annihilation rate can be enhanced in circular and spherical nanostructures.

Variation of Transmission Probability Spectrum with the Number of Dots in T-shaped Topology of Quantum Dot System

We analyze the transmission coefficient for T-shaped configuration for quantum dot systems by increasing the number of dots side coupled to the active dot. Analytical expressions for the transmission coefficient have been calculated, in the presence of on-dot Coulomb interaction, using non-equilibrium Green function techniques. The higher-order Green functions containing Coulomb interaction terms have been decoupled using the mean-field approximation. Numerical results show a systematic variation in the transmission peak structure as the number of quantum dots side coupled to the active dot increases. The energy levels of dots available for electron transport have been identified in terms of the internal parameters of quantum dot systems. It is found that the number of transmission probability peaks is directly related to the number of dots in the T-shaped quantum dot system.

Solvable model of gas production decline from hydrofractured networks.

We address questions that arose from studying gas and oil production from hydrofractured wells. Does past production predict the future? This depends on deducing from production as much as possible about the plausible geometries of the fracture network. We address the problem through a solvable model and use kinetic Monte Carlo and Green's function techniques to solve it. We have three main findings. First, at sufficiently long times, the production from all compact fracture networks is described by a universal function with two scaling parameters, one of which is the diffusivity of unbroken rock α and the second of which is a parameter V_{ext} with units of volume. Second, for fracture networks where the power-law distribution of fracture spacings falls below a critical value (and this appears to be the case in practice), early-time production always scales as one over the square root of time. Third, the diffusivity α that sets the scale for late-time production is inherently difficult to estimate from production data, but the methods here provide the best hope of obtaining it and thus can determine the physics that will govern the decline of unconventional gas and oil wells.

Heat transport in a two-level system driven by a time-dependent temperature

The field of thermotronics aims to develop thermal circuits that operate with temperature biases and heat currents just as how electronic circuits are based on voltages and electric currents. Here, we investigate a thermal half-wave rectifier based on a quantum two-level system (a qubit) that is driven by a periodically modulated temperature difference across it. To this end, we present a non-equilibrium Green's function technique, which we extend to the time domain to account for the time-dependent temperature in one of two thermal reservoirs connected to the qubit. We find that the qubit acts a thermal diode in parallel with a thermal capacitor, whose capacitance is controlled by the coupling to the reservoirs. These findings are important for the efforts to design non-linear thermal components such as heat rectifiers and multipliers that operate with more than one diode.

Gravitational radiation close to a black hole horizon: Waveform regularization and the out-going echo

Black hole perturbation theory for Kerr black holes is best studied in the Newman Penrose Formalism, in which gravitational waves are described as perturbations in the Weyl scalars $\psi_0$ and $\psi_4$, with the governing equation being the well-known Teukolsky equation. Near infinity and near horizon, $\psi_4$ is dominated by the component that corresponds to waves propagating towards the positive radial direction, while $\psi_0$ is dominated by the component that corresponds to waves that propagate towards the negative radial direction. Since gravitational-wave detectors measure out-going waves at infinity, research has been mainly focused on $\psi_4$, leaving $\psi_0$ less studied. But the scenario is reversed in the near horizon region where the in-going-wave boundary condition needs to be imposed. Thus, the near horizon phenomena, e.g., tidal heating and gravitational-wave echoes from Extremely Compact Objects (ECOs), require computing $\psi_0$. In this work, we explicitly calculate the source term for the $\psi_0$ Teukolsky equation due to a point particle plunging into a Kerr black hole. We highlight the need to regularize the solution of the $\psi_0$ Teukolsky equation obtained using Green's function techniques. We suggest a regularization scheme for this purpose and go on to compute the $\psi_0$ waveform close to a Schwarzschild horizon for two types of trajectories of the in-falling particle. We compare the $\psi_0$ waveform calculated directly from the Teukolsky equation with the $\psi_0$ waveform obtained by using the Starobinsky-Teukolsky identity on $\psi_4$. We also compute the out-going echo waveform near infinity, using the near-horizon $\psi_0$ computed directly from the Teukolsky equation and the Boltzmann boundary condition on the ECO surface. We show that this echo is quantitatively different (stronger) than the echo obtained using previous prescriptions. (abridged)