Phase diagrams of a ferroelectric superlattice: A Green’s function technique study

A Fermi-type Green’s function method has been used to investigate the phase transition properties of a ferroelectric superlattice with two alternating materials on the basis of the transverse Ising model. By performing a higher-order decoupling to the equations of motion for the Green’s functions, the eigenfrequencies of the infinite ferroelectric superlattice are obtained. Moreover, we discuss the dependence of the phase diagrams on the interface coupling strength, the transverse field, and the thicknesses of two slabs. The comparison between the Green’s function technique and the usual mean-field approximation is illustrated.     

Nonequilibrium spin transport through a diluted magnetic semiconductor quantum dot system with noncollinear magnetization

The spin-dependent transport through a diluted magnetic semiconductor quantum dot (QD) which is coupled via magnetic tunnel junctions to two ferromagnetic leads is studied theoretically. A noncollinear system is considered, where the QD is magnetized at an arbitrary angle with respect to the leads’ magnetization. The tunneling current is calculated in the coherent regime via the Keldysh nonequilibrium Green’s function (NEGF) formalism, incorporating the electron–electron interaction in the QD. We provide the first analytical solution for the Green’s function of the noncollinear DMS quantum dot system, solved via the equation of motion method under Hartree–Fock approximation. The transport characteristics (charge and spin currents, and tunnel magnetoresistance (TMR)) are evaluated for different voltage regimes. The interplay between spin-dependent tunneling and single-charge effects results in three distinct voltage regimes in the spin and charge current characteristics. The voltage range in which the QD is singly occupied corresponds to the maximum spin current and greatest sensitivity of the spin current to the QD magnetization orientation. The QD device also shows transport features suitable for sensor applications, i.e., a large charge current coupled with a high TMR ratio.     

Analytic and numeric Green’s functions for a two-dimensional electron gas in an orthogonal magnetic field

We have derived closed analytic expressions for the Green’s function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green’s functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green’s function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of the Green’s function has been performed by means of the decimation-renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green’s function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems.     

Effect of inelastic electron-phonon interaction on tunneling magnetoresistance through ferromagnetic-organic molecule-ferromagnetic junction

We have studied the effect of inelastic electron-phonon interaction on the spin-dependent transport properties of a molecule, trans-polyacetylene (trans-PA), as a molecular bridge sandwiched between two ferromagnetic (FM) electrodes. The work is based on a tight-binding Hamiltonian model within the framework of a generalized Green’s function technique and relies on the Landauer-Büttiker formalism as the basis for studying the current-voltage characteristic of this system. We use the wide-band approximation for FM electrodes. It is shown that due to inelastic interactions, the spin currents increase in a finite value of voltage and tunnel magnetoresistance (TMR) decreases compared with TMR obtained in the absence of phonons.     

A hybrid method for the parallel computation of Green’s functions

Quantum transport models for nanodevices using the non-equilibrium Green’s function method require the repeated calculation of the block tridiagonal part of the Green’s and lesser Green’s function matrices. This problem is related to the calculation of the inverse of a sparse matrix. Because of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green’s and lesser Green’s function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only require computing a small number of entries of the inverse matrix. Then, we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size.     

Spin transport in bimetallic pentalene complexes

Spin transport in bimetallic pentalene complexes (CpM(pentalene)M′Cp;M,M′=Fe,Co,Ni) between two gold electrodes was investigated, using a Green’s function formalism under density functional theory. Variation of the metal atom species in the complexes gives a considerable change in their spin properties, with hetero-bimetallic complexes containing an odd number of electrons exhibiting spin filter behaviour. In contrast, alternation in the contact condition, whether Cp-anchoring or adducting by sulphur-gold bonds, had almost no effect on spin filter behaviour, but did lead to variation in electrical conduction. We examined suitable bimetallic pentalene complexes in order to enhance their spin filter efficiency.     

Nonequilibrium spin-polarized transport through two parallel-coupled quantum dots

Spin-polarized transport through an Aharonov–Bohm ring containing two quantum dots (QDs) in each of its arms is studied by using the nonequilibrium Green’s function technique. We take both the Rashba spin-orbit interaction that exists in one of the QDs, and an inhomogeneous magnetic flux penetrating through the ring, into consideration. It is found that a 100% spin-polarized current can be driven out of the QDs ring, and both the spin directions and the magnitude of the outgoing current can be controlled. The origin of the pure spin-up or spin-down current is interpreted in terms of the spin accumulation in the QDs. This device is realizable by presently available technologies and can be used as a spin filter.     

Scalar Green’s function for penetrable or dielectric scatterers

In a series of former papers, we developed the so-called self-consistent Green’s function formalism (SGFF) for acoustic and light scattering on impenetrable or ideal metallic scatterers. With the paper at hand we will extend the application of this formalism to penetrable or dielectric scatterers. The concept of the Green’s function of the third kind is utilized which was introduced first by Tai. It must be slightly generalized to allow the treatment of nonspherical scatterers. The following considerations reveal the conceptual equivalence between the Green’s function of the third kind and Waterman’s T-matrix method. It is another goal of this paper to demonstrate that the conventional boundary and volume integral equations can be also derived within the developed Green’s function formalism.     

The shear viscosity of a two component Fermi gas with unequal population at low temperatures

The shear viscosity of spin-polarized Fermi gas at low temperatures is calculated by using the Green’s functions method. In the BEC limit where a Feshbach resonance gives rise to tightly bound dimer molecules, the contributions of the interactions between dimer-atom and imer-dimer take into account to the viscous relaxation rate.     

First-principles study of the electronic transport properties of a C131 -based molecular junction

Using first-principles density functional theory and the non-equilibrium Green’s function formalism, we have studied the electronic transport properties of the dumbbell-like fullerene dimer C₁₃₁-based molecular junction. Our results show that the current-voltage curve displays an obvious negative differential resistance phenomenon in a certain bias voltage range. The negative differential resistance behavior can be understood in terms of the evolution of the transmission spectrum and the projected density of states with applied bias voltage. The present findings could be helpful for the application of the C₁₃₁ molecule in the field of single molecular devices or nanometer electronics.     

Phonon scattering in harmonic model for a typical quantum wire

In this study, we extend a fully exact Green’s function formalism to calculate the phonon transmission coefficient in a short simulated chain. We obtain new analytical formulas for a uniform-mass and periodic-mass chain. The results for a simple chain show that the resonance peak will be appeared without gap but for the periodic chain the transmission coefficient contains a gap in the acoustic band of leads.     

Green function method study of the anisotropic ferromagnetic Heisenberg model on a square lattice

We study the phase diagram of the anisotropic ferromagnetic Heisenberg model on a square lattice. We use the double-time Green’s function method within the Callen decoupling approximation. The dependence of the Curie temperature T_c on the spin S and on the anisotropy parameter Δ (Δ=0 and 1 correspond to the isotropic Heisenberg and Ising model, respectively) is obtained explicitly. Our results are in agreement with results obtained from other theoretical approaches.     

Superoperator nonequilibrium Green’s function theory of many-body systems; applications to charge transfer and transport in open junctions

Nonequilibrium Green’s functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and introduce superoperator algebra that greatly simplifies the derivation and the physical interpretation of all quantities. Expressions for various observables are derived directly in real time in terms of superoperator nonequilibrium Green’s functions (SNGF), rather than the artificial time-loop required in Schwinger’s Hilbert-space formulation. Applications for computing interaction energies, charge densities, average currents, current induced fluorescence, electroluminescence and current fluctuation (electron counting) statistics are discussed.     

Boundary symmetries in linear differential and integral equation problems applied to the self-consistent Green’s function formalism of acoustic and electromagnetic scattering

Explicit symmetry relations for the Green’s function subject to homogeneous boundary conditions are derived for arbitrary linear differential or integral equation problems in which the boundary surface has a set of symmetry elements. For corresponding homogeneous problems subject to inhomogeneous boundary conditions implicit symmetry relations involving the Green’s function are obtained. The usefulness of these symmetry relations is illustrated by means of a recently developed self-consistent Green’s function formalism of electromagnetic and acoustic scattering problems applied to the exterior scattering problem. One obtains explicit symmetry relations for the volume Green’s function, the surface Green’s function, and the interaction operator, and the respective symmetry relations are shown to be equivalent. This allows us to treat boundary symmetries of volume-integral equation methods, boundary-integral equation methods, and the T matrix formulation of acoustic and electromagnetic scattering under a common theoretical framework. By specifying a specific expansion basis the coordinate-free symmetry relations of, e.g., the surface Green’s function can be brought into the form of explicit symmetry relations of its expansion coefficient matrix. For the specific choice of radiating spherical wave functions the approach is illustrated by deriving unitary reducible representations of non-cubic finite point groups in this basis, and by deriving the corresponding explicit symmetry relations of the coefficient matrix. The reducible representations can be reduced by group-theoretical techniques, thus bringing the coefficient matrix into block-diagonal form, which can greatly reduce ill-conditioning problems in numerical applications.     

Antisymmetrized Green’s function approach to (e, e′) reactions with a realistic nuclear density

A completely antisymmetrized Green’s function approach to the inclusive quasielastic (e, e′) scattering, including a realistic one-body density, is presented. The single-particle Green’s function is expanded in terms of the eigenfunctions of the non-hermitian optical potential. This allows one to treat final state interactions consistently in the inclusive and in the exclusive reactions. Nuclear correlations are included in the one-body density. Numerical results for the response functions of ¹⁶O and ⁴⁰Ca are presented and discussed.     

Electrical generation of pure spin current with oscillating spin-orbit interaction

We propose an electrical scheme for the generation of a pure spin current without a charge current in a two-terminal device, which consists of a scattering region of a two-dimensional electron gas (2DEG) with Rashba (R) and/or Dresselhaus (S) spin-orbit interaction (SOI) and two normal leads. The SOI is modulated by a time-dependent gate voltage to pump a spin current. Based on a tight-binding model and the Keldysh Green’s function technique, we obtain the analytical expression of the spin current. It is shown that a pure spin current can be pumped out, and its magnitude could be modulated by device parameters such as the oscillating frequency of the SOI, as well as the SOI strength. Moreover, the spin polarisation direction of the spin current could also be tuned by the strength ratio between RSOI and DSOI. Our proposal provides not only a fully electrical means to generate a pure spin current but also a way to control the spin polarisation direction of the generated spin current.     

Theory of inelastic tunneling spectroscopy of a single molecule - Competition between elastic and inelastic current

A theory of inelastic electron tunneling spectroscopy of a single molecule with scanning tunneling microscope is presented using the Keldysh Green’s function method for an adsorbate-induced resonance coupled to the molecular vibration. It is found that the correction to the tunneling current is expressed in terms of the transmission probability; the correction is negative for the elastic part of the current and positive for the inelastic one. The differential conductance (dI/dV) exhibits an increase or decrease at the threshold corresponding to the opening of inelastic channel depending on the sign of the correction, and the size of this conductance jump is scaled with the vibrational damping due to electron-hole pair excitation. The lineshape of d²I/dV²-spectra calculated using a renormalized adsorbate Green’s function evolves from an antisymmetric dip to a peak through the derivative-like one as the position of the adsorbate resonance recedes from the Fermi level of the substrate.     

Tuning of electron transport through a moebius strip: Shot noise

We study electron transport through a moebius strip attached to two metallic electrodes by the use of a Green’s function technique. A parametric approach is used based on the tight-binding model to characterize the electron transport through such a bridge system and it is observed that the transport properties are significantly affected by (a) the transverse hopping strength between the two channels and (b) the strip-to-electrodes coupling strength. In this context we also describe the noise power of the current fluctuations, which provide key information about the electron correlation which is obtained by calculating the Fano factor (F). The knowledge of these current fluctuations gives important ideas for the fabrication of efficient molecular devices.     

Exact and quasiclassical Green's functions of two-dimensional electron gas with Rashba–Dresselhaus spin–orbit interaction in parallel magnetic field

New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba–Dresselhaus spin–orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that allows an exact analytical solution is also highlighted. To demonstrate the advantages of our approach we apply the obtained Green's function to calculation of electron density and magnetization.     

Electronic charge transport through ZnO nanoribbons

I–V characteristics of ZnO nanoribbons (NRs) have been investigated using density functional theory coupled to non-equilibrium Green’s Function. The current through the NRs drops with the increasing NR width, leveling off to 1.66 and 0.42 µA in zig-zag and arm-chair NRs respectively for widths ~20 Å at 3 V of electrical bias. The transconductance as well as the current flowing through the arm-chair NRs decays exponentially with NR width for both odd and even number of dimer lines traversed. The current through the zig-zag NRs falls off exponentially with NR width, being insensitive to the odd or even numbers of zig-zag lines appearing along the normal to the charge transport direction.