Equations For Green Functions Research Articles

A spectral function for an interacting electron-lattice system

The lattice quasiparticle conserving Hamiltonian for an interacting electron-lattice system is employed in calculating the electromagnetic spectral response function in absorption for an electron located in a deep trap such that the electronic transition energies are much higher than the cutoff of the lattice vibrational spectrum. The zero-order Hamiltonian for the system is then diagonal in electronic quantum numbers and linear in the lattice vibrational mode coordinates. The spectral response is calculated for a dipole mediated transition by employing the temperature-dependent double-time Green's function technique. It is shown that because of the properties of the lattice field operators, the hierarchy of Green's function equations decouples and no higher-order Green's functions are required for obtaining an explicit solution to a given order. An exact solution for the absorption of spectrum in the lowest order in electromagnetic field is given in terms of delta-function lines. Broadening effects, numerical calculation restrictions and applications to molecular vibronic spectra are briefly discussed.

Development of an imaging modality utilizing 2D optical signals during an EPI-fluorescent optical mapping experiment

Optical mapping is a commonly used technique to visualize the electrical activity in the heart. Recently, several groups have attempted to use the signals acquired in optical mapping to image the transmembrane potential in the heart, which would be particularly advantageous when studying the effects of defibrillation-type shocks throughout the wall of the heart. Our work presents an alternative imaging method that makes use of data obtained using multiple wavelengths and therefore multiple optical decay constants. A modified form of the diffusion equation Green's function for a semi-infinite slab of tissue is derived and used to relate the detected optical signals to the source of emission photons. Images using the optical signals are reconstructed using Gaussian quadrature and matrix inversion. Our results show that images can be obtained for source terms located below the tissue surface. Furthermore, we demonstrate that our reconstruction method's susceptibility to noise can be alleviated using sophisticated matrix inverse techniques, such as singular value decomposition. Sources that rapidly decay with depth or are highly localized in the image plane require more sophisticated techniques (e.g., regularization methods) to image the electrical activity in the heart. The work presented here demonstrates the feasibility of a new imaging technique of cardiac electrical activity using optical mapping.

Exit Time, Green Function and Semilinear Elliptic Equations

Let $D$ be a bounded Lipschitz domain in $R^n$ with $n\geq 2$ and $\tau_D$ be the first exit time from $D$ by Brownian motion on $R^n$. In the first part of this paper, we are concerned with sharp estimates on the expected exit time $E_x [ \tau_D]$. We show that if $D$ satisfies a uniform interior cone condition with angle $\theta \in ( \cos^{-1}(1/\sqrt{n}), \pi )$, then $c_1 \varphi_1(x) \leq E_x [\tau_D] \leq c_2 \varphi_1 (x)$ on $D$. Here $\varphi_1$ is the first positive eigenfunction for the Dirichlet Laplacian on $D$. The above result is sharp as we show that if $D$ is a truncated circular cone with angle $\theta < \cos^{-1}(1/\sqrt{n})$, then the upper bound for $E_x [\tau_D]$ fails. These results are then used in the second part of this paper to investigate whether positive solutions of the semilinear equation $\Delta u = u^{p}$ in $ D,$ $p\in R$, that vanish on an open subset $\Gamma \subset \partial D$ decay at the same rate as $\varphi_1$ on $\Gamma$.

Scalar Casimir-Polder forces for uniaxial corrugations

We investigate the Dirichlet-scalar equivalent of Casimir-Polder forces between an atom and a surface with arbitrary uniaxial corrugations. The complexity of the problem can be reduced to a one-dimensional Green's function equation along the corrugation which can be solved numerically. Our technique is fully nonperturbative in the height profile of the corrugation. We present explicit results for experimentally relevant sinusoidal and sawtooth corrugations. Parameterizing the deviations from the planar limit in terms of an anomalous dimension which measures the power-law deviation from the planar case, we observe up to order-one anomalous dimensions at small and intermediate scales and a universal regime at larger distances. This large-distance universality can be understood from the fact that the relevant fluctuations average over corrugation structures smaller than the atom-wall distance.

Voltage-controllable spin-polarized transport through parallel-coupled double quantum dots with Rashba spin–orbit interaction

A spin device, consisting of parallel-coupled double quantum dots and three normal metal leads, is proposed to realize spin-polarized current without the help of magnetic field and magnetic material. Based on the Keldysh nonequilibrium Green function technique and equation of motion method, the spin-dependent current formula in each lead is derived. It is shown that not only a fully polarized current but also a tunable pure spin current can be obtained by modulating the structure parameters, strength of Rashba spin–orbit interaction and bias voltages properly. It further demonstrates the dependence of the spin-polarized current on the strength of the Rashba spin–orbit interaction.

Influence of inter cell resonant tunneling on the out-of-plane electronic transport behavior in layered high Tc cuprates

The influence of inter unit cell resonant tunneling between the copper-oxygen planes on the c-axis electronic conductivity (σc) in normal state of optimal doped bilayer high Tc cuprates like Bi2Sr2CaCu2O8+x is investigated using extended Hubbard Hamiltonian including resonant tunneling term (T12) between the planes in two adjoining cells. The expression for the out-of-plane (c-axis) conductivity is calculated within Kubo formalism and single particle Green's function by employing Green's function equations of motion technique within meanfield approximation. On the basis of numerical computation, it is pointed out that the renormalized c-axis conductivity \((\tilde {\sigma}_{c})\) increases exponentially with the increment in inter cell resonant tunneling. The effect of T12 on renormalized c-axis conductivity is found to be prominent at low temperatures as compared to temperatures above room temperature (~300 °K). The Coulomb correlation suppresses the variation of renormalized c-axis conductivity with temperature, while renormalized c-axis conductivity increases on increasing carrier concentration. These theoretical results are viewed in terms of existing c-axis transport measurements.

Spin Dynamics in (III,Mn)V Ferromagnetic Semiconductors: The Role of Correlations

We address the role of correlations between spin and charge degrees of freedom on the dynamical properties of ferromagnetic systems governed by the magnetic exchange interaction between itinerant and localized spins. For this we introduce a general theory that treats quantum fluctuations beyond the random phase approximation based on a correlation expansion of the Green's function equations of motion. We calculate the spin susceptibility, spin-wave excitation spectrum, and magnetization precession damping. We find that correlations strongly affect the magnitude and carrier concentration dependence of the spin stiffness and magnetization Gilbert damping.

Transient charging and discharging of spin-polarized electrons in a quantum dot

We study spin-polarized transient transport in a quantum dot coupled to two ferromagnetic leads subjected to a rectangular bias voltage pulse. Time-dependent spin-resolved currents, occupations, spin accumulation, and tunneling magnetoresistance (TMR) are calculated using both nonequilibrium Green function and master equation techniques. Both parallel and antiparallel leads' magnetization alignments are analyzed. Our main findings are: a dynamical spin accumulation that changes sign in time, a short-lived pulse of spin polarized current in the emitter lead (but not in the collector lead), and a dynamical TMR that develops negative values in the transient regime. We also observe that the intra-dot Coulomb interaction can enhance even further the negative values of the TMR.

A Self-Consistent Full 3-D Real-Space NEGF Simulator for Studying Nonperturbative Effects in Nano-MOSFETs

In this paper, we present a full 3-D real-space quantum-transport simulator based on the Green's function formalism developed to study nonperturbative effects in ballistic nanotransistors. The nonequilibrium Green function (NEGF) equations in the effective mass approximation are discretized using the control-volume approach and solved self-consistently with the Poisson equation in order to obtain the electron and current densities. An efficient recursive algorithm is used in order to avoid the computation of the full Green function matrix. This algorithm, and the parallelization scheme used for the energy cycle, allow us to compute very efficiently the current-voltage characteristic without the simplifying assumptions often used in other quantum-transport simulations. We have applied our simulator to study the effect of surface roughness and stray charge on the I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> -V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> characteristic of a 6-nm Si-nanowire transistor. The results highlight the distinctly 3-D character of the electron transport, which cannot be accurately captured by using 1-D and 2-D NEGF simulations, or 3-D mode-space approximations.

Rigorous derivation of the mean-field Green functions of the two-band Hubbard model of superconductivity

The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-Tc superconductivity in cuprates (Plakida et al 1995 Phys. Rev. B 51 16599, Plakida et al 2003 JETP 97 331) rests on the Hubbard operator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean-field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet-hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, an approximation procedure based on the identification and elimination of exponentially small quantities is described. It secures the reduction of the correlation order to GMFA-GF expressions.

Multiparticle tunnelling in diffusive superconducting junctions

We formulate a theoretical framework to describe multiparticle current transport in planarsuperconducting tunnel junctions with diffusive electrodes. The approach is based on thedirect solving of quasiclassical Keldysh–Green function equations for nonequilibriumsuperconductors, and consists of a combination of circuit theory analysis and improvedperturbation expansion. The theory predicts a much greater scaling parameter for thesubharmonic gap structure of the tunnel current in diffusive junctions compared to the onein ballistic junctions and mesoscopic constrictions with the same barrier transparency.

Quantum Simulation of Device Characteristics of Silicon Nanowire FETs

A quantum simulation of silicon nanowire field-effect transistors has been performed in the frame work of the effective mass theory, where the three-dimensional Poisson equation was solved self-consistently with the mode-space nonequilibrium Green's function equations in the ballistic transport regime. The dependence of the device performance on the gate length and width for three types of gate configuration has been studied, focusing on the contribution of the tunneling current to the total current. The effects of gate underlap and the corner rounding of silicon body on the device performance have been also investigated quantitatively, leading to the conclusions that the gate underlap is an important factor in improving the subthreshold characteristics of the device, but the corner rounding of silicon body is not a significant factor, especially for devices with silicon body width of a few nanometers

Two-particle approach to the electronic structure of solids: I: Scattering in the presence of the Coulomb interaction

Based on an extension of Hubbard’s treatment of the electronic structure of correlated electrons in matter we propose a methodology that incorporates the scattering off the Coulomb interaction through the determination of a two-particle propagator. The Green function equations of motion are then used to obtain single-particle Green functions and related properties such as densities of states. The solutions of the equations of motion in two- and single-particle spaces are accomplished through applications of the coherent potential approximation. The formalism is illustrated by means of calculations for a single-band model system representing a linear arrangement of sites with nearest neighbor hopping and an one-site repulsion when two electrons of opposite spin occupy the same site in the lattice in the manner described by the so-called Hubbard Hamiltonian.

Quantum criticality of a d-dimensional spin-S XXZ ferromagnetic model with longitudinal infinite-range interactions

A d-dimensional spin-S XXZ ferromagnetic model with uniform long-range interactions in the z-direction is mapped into an effective XY model in a transverse field. Then, using the two-time Green function equation of motion method, the zero-temperature properties for a periodic cubic lattice are exactly obtained close to the quantum critical point signaling the field-induced quantum phase transition from the fully polarized state into a phase with easy-plane spin ordering. We determine the relevant critical exponents which have a mean-field character for any d and S.

Supersymmetric low-energy theory and renormalization group for a clean Fermi gas with a repulsion in arbitrary dimensions

We suggest a new method of calculations for a clean Fermi gas with a repulsion in any dimension. This method is based on writing equations for quasiclassical Green functions and reducing them to equations for collective spin and charge excitations. The spin excitations interact with each other and this leads to non-trivial physics. Writing the solution of the equations and the partition function in terms of a functional integral over supervectors and averaging over fluctuating fields we come to an effective field theory describing the spin excitations. In some respects, the theory is similar to bosonization but also includes the ``ghost'' excitations which prevents overcounting of the degrees of freedom. Expansion in the interaction reveals logarithmic in temperature corrections. This enables us to suggest a renormalization group scheme and derive renormalization group equations. Solving these equations and using their solutions for calculating thermodynamic quantities we obtain explicit expression for the specific heat containing only an effective amplitude of the backward scattering. This amplitude has a complicated dependence on the logarithm of temperature, which leads to a non-trivial temperature dependence of the specific heat.

A NEGF study of the effect of surface roughness on CMOS nanotransistors

Start The effect of surface roughness on the electron transport of a double gate nanotransistor has been studied. The study has been carried out using a two-dimensional nonequilibrium Green's function formalism coupled self-consistently with Poisson's equation. A novel discretisation scheme for Poisson and the Green's function equations has been implemented in order to describe properly the surface roughness. The two-dimensional electron and current density landscape for the device with surface roughness exhibit strong inhomogeneity as compare with the smooth case (non-surface roughness). The effects of the specific profile of the surface roughness do not self-average. The total macroscopic current pattern follows the microscopic detail of the roughness.

Supersymmetric approximations to the 3D supersymmetricO(N)model

We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well as in the Hartree approximation, and derive the finite temperature renormalized effective potential. We derive the exact Schwinger-Dyson equations for the superfield Green functions and develop the machinery for going beyond the next to leading order in large-N approximation using a truncation of these equations which can also be derived from a two-particle irreducible effective action.

Performance of 2 nm gate length carbon nanotube field-effect transistors with source∕drain underlaps

The performance of coaxially gated, zero-Schottky-barrier, carbon nanotube field-effect transistors is investigated for gate lengths down to 2 nm with source and drain underlaps. Such devices can have nearly ideal subthreshold slopes of ∼63mV∕dec and maximum on∕off current ratios of 2.2×106 assuming 0.0–0.4 volt swing. The leakage mechanism is a combination of both intra-band and inter-band tunneling. For a 30 nm long carbon nanotube (CNT) with a 2 nm gate, Cg=3.13aF, the intrinsic switching time, τs=CgVDD∕ION, is 370 fs, and the intrinsic cut-off frequency defined by fT=gm∕(2πCg) is 1.6 THz. The ambipolar leakage current is suppressed by Coulomb blockade. Calculations are performed using a π-bond model and a self-consistent solution of the nonequilibrium Green function equations and Poisson’s equation.

Matrix technique for nonperturbative Green function of time-independent Schrödinger equation

A Green function of time-independent multi-channel Schrodinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multi-channel Schrodinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multi-channel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multi-potential system within quasi-classical approximation. The limits of strong and weak inter-channel interactions are studied.

New approach to the theory of lattice vibrations of random alloys

The theory of vibrational excitations of random alloys is presented, which takes into account the scattering of excitations on n-impurity complexes (clusters) and is capable to describe complex structure of their spectra. The essential feature of the theory consists in two-stage disorder averaging procedure. First, theory equations are averaged and Fourier transformed over the coordinate characterizing the cluster position as a whole. Then they are averaged over inter-impurity distances in the cluster. The derivation of the Green function equations is carried out both in the version similar to average-t-matrix approximation (ATA) and in that similar to coherent potential approximation (CPA). (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)