Green Function Treatment Research Articles

Spectro-spatial evolution of the CMB. Part II. Generalised Boltzmann hierarchy

In this paper, we formulate a generalised photon Boltzmann hierarchy that allows us to model the evolution and creation of spectral distortion anisotropies caused by energy release in the early Universe. We directly build on our first paper in this series, extending the thermalisation Green's function treatment to the anisotropic case. We show that the problem can be described with the common Boltzmann hierarchy for the photon field extended by new spectral parameters — a step that reduces the complexity of the calculation by at least two orders of magnitude. Our formalism describes the effects of i) Doppler and potential driving, ii) spectral evolution by Compton scattering, iii) perturbed thermalisation and iv) anisotropic heating on the distortion anisotropies. We highlight some of the main physical properties of the equations and also outline the steps for computing CMB power spectra including distortion anisotropies. Limitations and extensions of the formulation are also briefly discussed. The novel Boltzmann hierarchy given here is the basis for a series of companion papers studying how distortion anisotropies evolve in the perturbed Universe and which physical processes could be constrained using future CMB imaging techniques.

Green's-function treatment of Rydberg molecules with spins

Green's-function treatment of Rydberg molecules with spins

Green Function Treatment of the Barocaloric Effect in Mn3GaN

Following our previous work on the magnetocaloric compounds FeMnAsxP[Formula: see text], we obtain thermomagnetic properties for the barocaloric antiperovskite Mn3GaN, which has been investigated in recent years in view of its thermal response under pressure cycling. Its structure displays canting of spins and a volume dilation in the antiferromagnetic (AFM) transition, related to magnetoelastic coupling. A random-phase-approximation (RPA) Green function theoretical treatment is applied to a two-exchange parameter Heisenberg model, and the canting of the spins orientation in the (111) planes of the structure is considered in the model. The observed first-order AFM phase transitions are reproduced by the introduction of a biquadratic spin term in the Hamiltonian, coupled to the volume dilation in the transition. The model is able to predict a greater stability for the canted spin structure as compared with conventional AFM, if the magnitudes of Mn magnetic moments in these structures are taken from the literature. The calculations of quantities of interest for barocaloric applications reproduce quite well the available data on temperature changes and latent heat under pressure cycling, at adiabatic and isothermal conditions, respectively.

Pump-driven normal-to-excitonic insulator transition: Josephson oscillations and signatures of BEC-BCS crossover in time-resolved ARPES

We consider a ground-state wide-gap band insulator turning into a nonequilibrium excitonic insulator (NEQ-EI) upon visiting properly selected and physically relevant highly excited states. The NEQ-EI phase, characterized by self-sustained oscillations of the complex order parameter, neatly follows from a Nonequilibrium Green's Function treatment on the Konstantinov-Perel' contour. We present the first {\em ab initio} band structure of LiF, a ground-state bulk insulator, in different NEQ-EI states and show that these states can be generated by currently available pump pulses. We highlight two general features of time-resolved ARPES spectra: (1) during the pump-driving the excitonic spectral structure undergoes a convex-to-concave shape transition and {\em concomitantly} the state of the system goes through a BEC-BCS crossover; (2) attosecond pulses shone after the pump-driving at different times $t_{\rm delay}$ generate a photocurrent which {\em oscillates} in $t_{\rm delay}$ with a pump-tunable frequency -- we show that this phenomenon is similar to the AC response of an exotic Josephson junction.

Gauge-invariant Green function dynamics: A unified approach

We present a gauge-invariant description of Green function dynamics introduced by means of a generalized Peirels phase involving an arbitrary differentiable path in space–time. Two other approaches to formulating a gauge-invariant description of systems, the Green function treatment of Levanda and Fleurov [M. Levanda, V. Fleurov, J. Phys.: Condens. Matter 6 (1994) 7889] and the usual multipolar expansion for an atom, are shown to arise as special cases of our formalism. We argue that the consideration of paths in the generalized Peirels phase that do not lead to introduction of an effective gauge-invariant Hamiltonian with polarization and magnetization fields may prove useful for the treatment of the response of materials with short electron correlation lengths.

Tensorial green-function theory of atomic-wire T-junction transmission

A tensorial Green-function treatment of the electronic transmission properties of an atomic wire T-junction is presented within the framework of the tight-binding approximation. The adoption of the tensorial formalism enables overlap effects to be included in a straightforward manner, without the need to resort to a change in the Hilbert space. The T-junction structure and the presence of overlap effects both give rise to antiresonances. Although those due to the former are located inside the energy band, the latter appear at the band edges. The transmission is seen to depend in different ways on the bond energy and the overlap between the attached atom and the wire. © 2012 Wiley Periodicals, Inc.

Nonequilibrium Green's function treatment of a new nanoscale dual-material double-gate MOSFET

In this paper the electrical characteristics of a novel nanoscale double-gate (DG) silicon-on-insulator(SOI) MOSFET, in which the front gate consists of two materials with different work functions, have been investigated by a full quantum-mechanical simulation. The simulations have been done by the self-consistent solution of 2D Poisson–Schrödinger equations, within the nonequilibrium Green's function (NEGF) formalism. The quantum simulation results show that the new structure decreases significantly the leakage current and drain conductance and increases the on–off current ratio and voltage gain as compared to the conventional DG SOI MOSFET. In this new structure, the potential in the channel region exhibits a step function that ensures the screening of the drain potential variation by the gate near the drain, resulting in suppressed short-channel effects like the drain-induced barrier lowering (DIBL) and hot-carrier effect.

Green function treatment of electronic transport in narrow rough semiconductor conduction channels

We explore the effect of geometrical fluctuations on the electronic transport in rough Si nanowire (NW) thermoelectric devices of diameter D < 10 nm. At this scale, the quantum nature of transport is accounted in the computation of energy dependent transmission coefficients through a recursive green function algorithm. The rough 3D NW geometry is used as a direct input to simulations through the roughness height Δ and autocovariance length L. Using a non parabolic band structure, the channel conductance above 0.1 eV is drastically reduced in such NW with high D/Δ ratio. In addition, the roughness induced resistivity is only increased by 6% on the first energy level of 10 nm Si channels with Δ = 7.7 Å, showing possible application for high thermoelectric figures of merit ZT.

The paramagnetic properties of one-dimensional spin-1 single-ion anisotropic ferromagnet

One-dimensional single-ion anisotropic ferromagnet with spin-1 is investigated by means of Green's function treatment in this paper. The model Hamiltonian includes a Heisenberg ferromagnetic term, an external magnetic field, and a second-order single-ion anisotropy. The magnetic properties of the system are treated by the random phase approximation for the exchange interaction term and the Anderson–Callen approximation for the anisotropy term. Our paramagnetic results are in agreement with the other theoretical results.

On magnon energy branches of multilayer ferrimagnetic superlattices [Reply to the comment “Boson Green's functions treatment of three‐layer ferrimagnetic superlattice”, phys. stat. sol. (b) 244, No. 10, 3750–3753 (2007)

AbstractThe magnon energy branches of multilayer ferrimagnetic superlattices are discussed, as regards the linear spin‐wave approach and Green's function technique. It is argued that negative energy branches in the spin‐wave spectra of the ferrimagnetic systems have physical significance, which is responsible for the zero‐point motion (i.e. the quantum fluctuations) in the ground state, since the sign of ωl(k) indicates the direction in which the spin‐wave mode propagates. On boson Green's function treatment, the results calculated for physical properties with consideration of negative energy spectra are correct and the consequent conclusions do not need to be re‐examined. Even for the definition of energy gaps, nothing is wrong from the theoretical point of view if one considers both negative and positive energy spectra, but one may need to consider two different definitions (one considers the negative/positive energy spectra; the other only the positive ones), from the experimental point of view, to compare both of them with experimental data, in an attempt to detect whether the negative energy branch does excite or not. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

TWO-DIMENSIONAL ANISOTROPIC HEISENBERG FERROMAGNET IN COEXISTING TRANSVERSE AND LONGITUDINAL MAGNETIC FIELDS

The two-dimensional spin-1/2 anisotropic Heisenberg ferromagnet is investigated in coexisting transverse and longitudinal magnetic fields. Using the Green function treatment, the magnetization and susceptibility are studied as a function of temperature, anisotropy and magnetic fields. The effects of exchange anisotropy and transverse magnetic field on the magnetic properties of the system are discussed.

Nonequilibrium Green's Function Treatment of Phonon Scattering in Carbon-Nanotube Transistors

We present the detailed treatment of dissipative quantum transport in carbon nanotube field-effect transistors (CNTFETs) using the non-equilibrium Green's function formalism. The effect of phonon scattering on the device characteristics of CNTFETs is explored using extensive numerical simulation. Both intra-valley and inter-valley scattering mediated by acoustic (AP), optical (OP), and radial breathing mode (RBM) phonons are treated. Realistic phonon dispersion calculations are performed using force-constant methods, and electron-phonon coupling is determined through microscopic theory. Specific simulation results are presented for (16,0), (19,0), and (22,0) zigzag CNTFETs that are in the experimentally useful diameter range. We find that the effect of phonon scattering on device performance has a distinct bias dependence. Up to moderate gate biases the influence of high-energy OP scattering is suppressed, and the device current is reduced due to elastic back-scattering by AP and low-energy RBM phonons. At large gate biases the current degradation is mainly due to high-energy OP scattering. The influence of both AP and high-energy OP scattering is reduced for larger diameter tubes. The effect of RBM mode, however, is nearly independent of the diameter for the tubes studied here.

Field dependence of the susceptibility maximum in the anisotropic Heisenberg ferromagnet

The location and height of the susceptibility maximum for anisotropic one and two-dimensional spin S = 1 2 Heisenberg models are investigated by using the Green's function treatment within the random phase approximation. The results are fitted to the power law behaviors, T m χ - T 0 = ah γ and χ ( T m χ ) = bh - β , in the high field. And the exponents γ , β are found to be dependent of the anisotropy. Our results do not support the 2 3 power laws which are obtained from the mean-field Landau's theory. For the isotropic and Ising cases, the exponents γ , β which are in agreement with the results by other theoretic techniques.

Identifying Contact Effects in Electronic Conduction throughC60on Silicon

We present a theory of current conduction through buckyball (C(60)) molecules on silicon by coupling a density functional treatment of the molecular levels embedded in a semiempirical treatment of the silicon surface with a nonequilibrium Green's function treatment of quantum transport. Several experimental variations in conductance-voltage characteristics are quantitatively accounted for by varying the detailed molecule-silicon bonding geometries. We identify how variations in contact surface microstructure influence the number, positions, and shapes of the conductance peaks, while varying separations of the scanning probe from the molecules influence their peak amplitudes.

A self-consistent transport model for molecular conduction based on extended Hückel theory with full three-dimensional electrostatics

We present a transport model for molecular conduction involving an extended Hückel theoretical treatment of the molecular chemistry combined with a nonequilibrium Green's function treatment of quantum transport. The self-consistent potential is approximated by CNDO (complete neglect of differential overlap) method and the electrostatic effects of metallic leads (bias and image charges) are included through a three-dimensional finite element method. This allows us to capture spatial details of the electrostatic potential profile, including effects of charging, screening, and complicated electrode configurations employing only a single adjustable parameter to locate the Fermi energy. As this model is based on semiempirical methods it is computationally inexpensive and flexible compared to ab initio models, yet at the same time it is able to capture salient qualitative features as well as several relevant quantitative details of transport. We apply our model to investigate recent experimental data on alkane dithiol molecules obtained in a nanopore setup. We also present a comparison study of single molecule transistors and identify electronic properties that control their performance.

SUPERCELL RHEED CALCULATIONS

Efficient calculational techniques for reflection high energy electron diffraction (RHEED) are reported for surfaces with large periodic supercells. A fast Fourier transform approach enables the computer time scaling of a conventional RHEED calculation to be reduced to n2 log (n), where n is the number of diffracted beams used in the calculation. The special technique needed to implement this for arbitrary incident azimuths with symmetry optimization is detailed. A Green's function method is also introduced which is particularly suitable for calculations for imperfect surfaces. This combines the conventional approach to RHEED for dealing with substrate diffraction with a Green's function treatment for an imperfect surface of supercells and has n log (n) time scaling. Techniques for matching the results of the conventional and Green's function treatments at the substrate–surface interface are given. In addition, numerical procedures for solving the resulting equations are described and a selection of illustrative results is presented.

Theoretical analysis of the 4He( K−, π∓) spectrum

We report phenomenological study of the 4He(in-flight K −, π ∓) data at BNL, in order to clarify the structure of Σ 4He ( J π =0 +, T⋍ 1 2 ) which was predicted theoretically as a Σ-hypernuclear bound state. The π ∓ spectrum is calculated in the DWIA framework by Green's function treatment with the Λ-Σ coupling, and is compared with the data. The result shows us the structure of Σ 4He as a bound state.

Resonant electron-phonon coupling: Magnetopolarons in InP.

We present a theoretical analysis of recent experimental data on resonant magnetopolarons in InP. These effects appear as strong anticrossings in Landau-level fan plots obtained from magneto-Raman profiles of the longitudinal-optic (LO)-phonon scattering intensity vs magnetic field. We calculate renormalized Landau levels using electron self-energies due to Fr\"ohlich electron--LO-phonon interaction, and find an analytical expression for the self-energy of the magnetopolaron quasiparticle. A Green's-function treatment leads to close agreement with the experiment, even though we use relatively simple approximations for the self-energy. We find that the data can only be explained when couplings between adjacent Landau levels are taken into account. At this point our model supersedes previous theories, where resonant magnetopolarons have been approximated by two-level systems. \textcopyright{} 1996 The American Physical Society.

An electrostatic interpretation of the weighted flow theorem of electromagnetic flowmeters

The weighted flow theorem of electromagnetic flowmeters links the output voltage of an electromagnetic flowmeter with the spatial velocity distribution of a fluid and the weight function. The existing derivations of the theorem are based on a formal Green's function treatment of the underlying partial differential equation describing flowmeter operation. The main aim of this paper is to provide a physically transparent and mathematically rigorous picture of the origin of the flowmeter output voltage. We show that electrostatic charges build up both in the volume of the meter and on its surfaces as a weakly conductive fluid enters the magnetic field of the meter. The flowmeter output voltage is completely determined by these volume and surface charges. Departing from the physical conditions in the fluid and the fluid boundaries we establish relations satisfied by those charge densities and then derive the analytical expression for the output voltage by standard electrostatic methods. The resulting expression is transformed into a volume integral of the scalar product of fluid velocity and the weight vector which in turn is equal to the vector product of the magnetic induction and a virtual current, as introduced by Bevir for the first time. We further show that this latter quantity may be interpreted as that part of the normalized current density of the operating flowmeter the contours of which are closed outside of the fluid. We also give a simple interpretation of the results based on conservation of energy. We hope that the proposed electrostatic approach could provide a more intuitive insight into flowmeter operation to electrical engineers than the general Green's function formalism.

Formation of the Σ4He hypernucleus by in-flight K − capture

The Σ-hypernuclear production by the in-flight 4He(K −, π −) reaction is investigated in the framework of a DWIA Green function treatment. A complex nucleus-Σ potential is derived from a realistic ΣN interaction; its real part is repulsive near the nuclear centre, which suppresses the ΣN→ΛN conversion. The resultant formation spectrum at P K−=450MeV/c exhibits a narrow peak below the Σ-emission threshold. This in-flight experiment is expected to provide more definitive information on the structure of the σ4He hypernucleus than the stopped K − experiment done at KEK.