Green Function Technique Research Articles

Theory of charge transport in molecular junctions: Role of electron correlation.

We extend the quasi-particle renormalized perturbation theory developed in our previous work [Y.-W. Chang and B.-Y. Jin, J. Chem. Phys. 141, 064111 (2014)] based on nonequilibrium Green's function techniques to study the effects of electron correlation on the charge transport process in molecular junctions. In this formalism, the single-impurity Anderson's model is used as the zeroth-order Hamiltonian of each channel orbital, and the inter-channel interactions are treated by perturbation corrections. Within this scheme, the on-channel Coulomb repulsion and the single-particle spectral line-broadening can be incorporated in the zeroth-order approximation, and thus the Coulomb blockade and coherent tunneling through individual channels can be described properly. Beyond the zeroth-order description, electron correlation can be included through the self-energy corrections in the forms of the second-Born approximation and the GW approximation. The effects of electron correlation on molecular junctions are manifested as the orbital energy correction, correlated transport process, and collisional line-broadening. As an application, we have applied the present formalism to phenyl-based molecular junctions described by the Pariser-Parr-Pople Hamiltonian. The signatures of electron correlation in the simulated current-voltage curves are identified and discussed.

Generation of Fabry–Pérot oscillations and Dirac state in two-dimensional topological insulators by gate voltage**Project supported by the National Natural Science Foundation of China (Grant Nos. U1404108, 11104072, and 10947162) and Henan Foundation and Frontier Technology Research Program of China (Grant No. 162300410056).

We investigate electron transport through HgTe ribbons embedded by strip-shape gate voltage through using a non-equilibrium Green function technique. The numerical calculations show that as the gate voltage is increased, an edge-related state in the valence band structure of the system shifts upwards, then hangs inside the band gap and merges into the conduction band finally. It is interesting that as the gate voltage is increased continuously, another edge-related state in the valence band also shifts upwards in the small-k region and contacts the previous one to form a Dirac cone in the band structure. Meanwhile in this process, the conductance spectrum displays as multiple resonance peaks characterized by some strong antiresonance valleys in the band gap, then behaves as Fabry–Pérot oscillations and finally develops into a nearly perfect quantum plateau with a value of . These results give a physical picture to understand the formation process of the Dirac state driven by the gate voltage and provide a route to achieving particular quantum oscillations of the electronic transport in nanodevices.

Spin heat capacity of monolayer and AB-stacked bilayer MoS2 in the presence of exchange magnetic field

Dirac theory and Green's function technique are carried out to compute the spin dependent band structures and corresponding electronic heat capacity (EHC) of monolayer (ML) and AB-stacked bilayer (BL) molybdenum disulfide (MoS2) two-dimensional (2D) crystals. We report the influence of induced exchange magnetic field (EMF) by magnetic insulator substrates on these quantities for both structures. The spin-up (down) subband gaps are shifted with EMF from conduction (valence) band to valence (conduction) band at both Dirac points in the ML because of the spin-orbit coupling (SOC) which leads to a critical EMF in the K point and EHC returns to its initial states for both spins. In the BL case, EMF results split states and the decrease (increase) behavior of spin-up (down) subband gaps has been observed at both K and K′ valleys which is due to the combined effect of SOC and interlayer coupling. For low and high EMFs, EHC of BL MoS2 does not change for spin-up subbands while increases for spin-down subbands.

Spin Hall effect and spin swapping in diffusive superconductors

We consider the spin-orbit-induced spin Hall effect and spin swapping in diffusive superconductors. By employing the non-equilibrium Keldysh Green's function technique in the quasiclassical approximation, we derive coupled transport equations for the spectral spin and particle distributions and for the energy density in the elastic scattering regime. We compute four contributions to the spin Hall conductivity, namely, skew scattering, side-jump, anomalous velocity, and the Yafet contribution. The reduced density of states in the superconductor causes a renormalization of the spin Hall angle. We demonstrate that all four of these contributions to the spin Hall conductivity are renormalized in the same way in the superconducting state. In its simplest manifestation, spin swapping transforms a primary spin current into a secondary spin current with swapped current and polarization directions. We find that the spin-swapping coefficient is not explicitly but only implicitly affected by superconducting correlations through the renormalized diffusion coefficients. We discuss experimental consequences for measurements of the (inverse) spin Hall effect and spin swapping in four-terminal geometries. In our geometry, below the superconducting transition temperature, the spin-swapping signal is increased an order of magnitude while changes in the (inverse) spin Hall signal are moderate.

General Green's function formalism for layered systems: Wave function approach

The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency and is limited to relatively small systems. Here we present a numerically efficient and physically transparent GF formalism for a general layered structure. In contrast to the recursive GF that directly calculates the GF through the Dyson equations, our approach converts the calculation of the GF to the generation and subsequent propagation of a scattering wave function emanating from a local excitation. This viewpoint not only allows us to reproduce existing results in a concise and physically intuitive manner, but also provides analytical expressions of the GF in terms of a generalized scattering matrix. This identifies the contributions from each individual scattering channel to the GF and hence allows this information to be extracted quantitatively from dual-probe STM experiments. The simplicity and physical transparency of the formalism further allows us to treat the multiple reflection analytically and derive an analytical rule to construct the GF of a general layered system. This could significantly reduce the computational time and enable quantum transport calculations for large samples. We apply this formalism to perform both analytical analysis and numerical simulation for the two-dimensional conductance map of a realistic graphene p-n junction. The results demonstrate the possibility of observing the spatially-resolved interference pattern caused by negative refraction and further reveal a few interesting features, such as the distance-independent conductance and its quadratic dependence on the carrier concentration, as opposed to the linear dependence in uniform graphene.

Spin filter properties of armchair graphene nanoribbons with substitutional Fe atoms

ABSTRACTThe spin filter capability of a (0,8) armchair graphene nanoribbon with Fe atoms at substitutional sites is investigated by density functional theory in combination with the non-equilibrium Green's function technique. For specific arrangements, a high degree of spin polarisation is achieved. These include a single substitution at an edge position or double substitution in the central sector of the transmission element. The possibility of switching between majority and minority spin polarisation by changing the double substitution geometry is predicted. Including the bias dependence of the transmission function proves to be essential for correct representation of the spin-resolved current-voltage profiles.

Effect of external magnetic field on the coexistence of SC and AFM in iron based superconductors

We have studied the interplay of antiferromagnetism and superconductivity in presence of an applied external magnetic field for the iron based superconductors. For the purpose we have proposed a model Hamiltonian and solved it self-consistently by using the Zubarev's technique of double time Green's function technique. The self-consistent gap equations are solved numerically and interpreted the gap values from the of density of states plots.

A Green's function approach to the nonrelativistic radial wave equation of hydrogen atom

We report an efficient and consistent method for the solution of Schrödinger wave equation using the Green's function technique and its successful application to the nonrelativistic radial wave equation of hydrogen atom. For the radial wave equation, the Green's function is worked out analytically by means of Laplace transform method and the wave function is proposed under the boundary conditions. Computationally the product of potential term, the proposed wave function and the Green's function are integrated iteratively to get the nonrelativistic radial wave function. The resultant wave after each iteration is normalized and plotted against the standard nonrelativistic radial wave function. The solution converges to the standard wave with the increasing number of iterations. Results are verified for the first 15 states of hydrogen atom. The method adopted here can be extended to many‐body problem and hope that it can enhance our knowledge about complex systems.

The electronic properties, electronic heat capacity and magnetic susceptibility of monolayer boron nitride graphene-like structure in the presence of electron-phonon coupling

In this work, we have studied the influences of electron-phonon (e-ph) coupling and chemical potential on the boron nitride graphene-like sheet. In particular, by starting the Green's function technique and Holstein model, the electronic density of states (DOS), electronic heat capacity (EHC) and magnetic susceptibility (MS) of this system have been investigated in the context of self-consistent second order perturbation theory which has been implemented to find the electronic self-energy. Our findings show that the band gap size decreases (increases) with e-ph coupling (chemical potential) parameters. The Schottky anomaly (crossover) decreases in EHC (MS) as soon as e-ph coupling increases. Also, the corresponding temperature with Schottky anomaly is considerably affected by e-ph coupling.

Electronic transport in disordered MoS2 nanoribbons

We study the electronic structure and transport properties of zigzag and armchair monolayer molybdenum disulfide nanoribbons using an 11-band tight-binding model that accurately reproduces the material's bulk band structure near the band gap. We study the electronic properties of pristine zigzag and armchair nanoribbons, paying particular attention to the edges states that appear within the MoS$_2$ bulk gap. By analyzing both their orbital composition and their local density of states, we find that in zigzag-terminated nanoribbons these states can be localized at a single edge for certain energies independent of the nanoribbon width. We also study the effects of disorder in these systems using the recursive Green's function technique. We show that for the zigzag nanoribbons, the conductance due to the edge states is strongly suppressed by short-range disorder such as vacancies. In contrast, the local density of states still shows edge localization. We also show that long-range disorder has a small effect on the transport properties of nanoribbons within the bulk gap energy window.

Influence of pairing correlations on the radius of neutron-rich nuclei

The influence of pairing correlations on the neutron root mean square (rms) radius of nuclei is investigated in the framework of self-consistent Skyrme Hartree-Fock-Bogoliubov calculations. The continuum is treated appropriately by the Green's function techniques. As an example the nucleus $^{124}$Zr is treated for a varying strength of pairing correlations. We find that, as the pairing strength increases, the neutron rms radius first shrinks, reaches a minimum and beyond this point it expands again. The shrinkage is due to the the so-called `pairing anti-halo effect', i. e. due to the decreasing of the asymptotic density distribution with increasing pairing. However, in some cases, increasing pairing correlations can also lead to an expansion of the nucleus due to a growing occupation of so-called `halo' orbits, i.e. weakly bound states and resonances in the continuum with low-$\ell $ values. In this case, the neutron radii are extended just by the influence of pairing correlations, since these `halo' orbits cannot be occupied without pairing. The term `anti-halo effect' is not justified in such cases. For a full understanding of this complicated interplay self-consistent calculations are necessary.

Copper adatoms on graphene: Theory of orbital and spin-orbital effects

We present a combined DFT and model Hamiltonian analysis of spin-orbit coupling in graphene induced by copper adatoms in the bridge and top positions, representing isolated atoms in the dilute limit. The orbital physics in both systems is found to be surprisingly similar, given the fundamental difference in the local symmetry. In both systems the Cu p and d contributions at the Fermi level are very similar. Based on the knowledge of orbital effects we identify that the main cause of the locally induced spin-orbit couplings are Cu p and d orbitals. By employing the DFT+U formalism as an analysis tool we find that both the p and d orbital contributions are equally important to spin-orbit coupling, although p contributions to the density of states are much higher. We fit the DFT data with phenomenological tight-binding models developed separately for the top and bridge positions. Our model Hamiltonians describe the low-energy electronic band structure in the whole Brillouin zone and allow us to extract the size of the spin-orbit interaction induced by the local Cu adatom to be in the tens of meV. By application of the phenomenological models to Green's function techniques, we find that copper atoms act as resonant impurities in graphene with large lifetimes of 50 and 100~fs for top and bridge, respectively.

Green's function approach to study the propagation of SH-wave in piezoelectric layer influenced by a point source

Green's function technique serves as a powerful tool to find the particle displacements due to SH-wave propagation in layer of a shape different from the space between two parallel planes. Therefore, the present paper undertook to study the propagation of SH-wave in a transversely isotropic piezoelectric layer under the influence of a point source and overlying a heterogeneous substrate using Green's function technique. The coupled electromechanical field equations are solved with the aid of Green's function technique. Expression for displacements in both layer and substrate, scalar potential and finally the dispersion relation is obtained analytically for the case when wave propagates along the direction of layering. Numerical computations are carried out and demonstrated with the aid of graphs for six different piezoelectric materials namely PZT-5H ceramics, Barium titanate (BaTiO3) ceramics, Silicon dioxide (SiO2) glass, Borosilicate glass, Cobalt Iron Oxide (CoFe2O4), and Aluminum Nitride (AlN). The effects of heterogeneity, piezoelectric and dielectric constants on the dispersion curve are highlighted. Moreover, comparative study is carried out taking the phase velocity for different piezoelectric materials on one hand and isotropic case on the other. Dispersion relation is reduced to well-known classical Love wave equation with a view to illuminate the authenticity of problem. Copyright © 2017 John Wiley & Sons, Ltd.

Shear Wave Propagation Due to a Point Source

The present paper is concerned with the propagation of shear waves in a heterogeneous isotropic layer lying over a semi-infinite homogeneous isotropic half-space due to a point source. The dispersion equation of shear waves has been established with the help of Green's function technique and Fourier transform. The deduced dispersion equation for this study agrees well with the classical Love wave equation in the absence of heterogeneity. Significant effect of heterogeneity on the phase velocity of shear wave has been observed. The dimensionless phase velocity against dimensionless wave number has been plotted and the influence of heterogeneity parameter is also revealed graphically through numerical computation.

Spin and charge Nernst effect in a four-terminal double quantum dot system

With the increase of integration scale, heat dissipation becomes one of the major problems in high density electronic devices and circuits. Controlling and reusing the heat energy in such miniaturized structures are essential topics for current and future technologies. With the development of microfabrication technology and low-temperature measurement technology in the last two decades, the thermoelectric measurement in low-dimensional sample has been feasible, and the thermal transport has received more and more attention. For the multi-terminal device, there is a novel thermoelectric phenomenon, called the spin Nernst effect, in which spin currents (or spin voltages) are generated perpendicularly to the temperature gradient. The spin Nernst effect has been confirmed experimentally, and has been theoretically studied in a variety of materials. In this paper, the spin and charge Nernst effect in a pair of vertically aligned quantum dots attached to four leads are studied in the Coulomb blockade regime based on the nonequilibrium Green's function technique. We focus on the influences of magnetic configuration and intra-dot (inter-dot) Coulomb interaction on the spin and charge Nernst effect. It is found that the signs and the magnitudes of spin and charge Nernst effect can be modulated by adjusting the magnetization directions of ferromagnetic electrodes. When the magnetic moments in the 1 and 3 electrodes are turned to antiparallel alignment, the pure spin Nernst (without charge Nernst) effect can occur by applying a transverse temperature gradient. Conversely, the spin and charge Nernst effect disappear if the magnetic moments of lead 1 and lead 3 are in the case of parallel configuration. Except for left and right thermal leads, we investigate the effect of the middle lead (lead 4) on the property of the Nernst effect. We find that when the normal metal lead 4 is transferred to ferromagnetic metal, the spin and charge Nernst effect both can be obtained simultaneously. In the end of the paper, we study the influences of intra-dot and inter-dot Coulomb interaction on the spin dependent Nernst coefficient. Through numerical calculations, we demonstrate that the magnitude of the Nernst effect is less dependent on the polarization strength of ferromagnetic electrodes, but can be remarkably enhanced by the Coulomb blockade. The spin Nernst coefficient is predicted to be more than two orders of magnitude larger than that of the case of zero Coulomb interaction. All the results indicate that the proposed four-terminal double quantum dot nano system is a promising candidate for spin caloritronic device.

New micromechanical modeling of the elastic behavior of composite materials with ellipsoidal reinforcements and imperfect interfaces

In this work, a new micromechanical model to determine the effective elastic behavior of composite materials with ellipsoidal reinforcements and imperfect interfaces is developed. By using the Green's functions technique, the integral equation of the linear elastic medium is reformulated in the presence of imperfect interfaces. The integral equation is then solved in the case of an ellipsoidal inclusion embedded in an infinite matrix with imperfect interface. By introducing the concept of interior and exterior-point Eshelby tensors, the solution of the inclusion problem is obtained in the case of displacement discontinuities and continuous traction across the interface between inclusion and matrix. The concentration equations are then exactly expressed in the general case of anisotropic elastic behavior and ellipsoidal inclusions with imperfect interface. In the case of spring interface model, the explicit concentration equations are obtained. In the case of isotropic elasticity, we retrieved the analytical strain concentration tensors from the literature for spherical inclusion morphology. The Mori-Tanaka homogenization scheme is used to determine the local strain and stress fields in each phase and effective elastic moduli of composite materials. In the case of fibrous composites under plane strain loading, the effective elastic moduli are successfully compared to those obtained by complex variable methods. The combined influence of shape of inclusions and interface parameters is analyzed on the effective elastic behavior.

Green's functions technique for calculating the emission spectrum in a quantum dot-cavity system

We introduce the Green's functions technique as an alternative theory to the quantum regression theorem formalism for calculating the two-time correlation functions in open quantum systems at the steady state. In order to investigate the potential of this theoretical approach, we consider a dissipative system composed of a single quantum dot inside a semiconductor cavity and the emission spectrum is computed due to the quantum dot as well as the cavity. We propose an algorithm based on the Green's functions technique for computing the emission spectrum that can easily be adapted to more complex open quantum systems. We found that the numerical results based on the Green's functions technique are in perfect agreement with the quantum regression theorem formalism. Moreover, it allows overcoming the inherent theoretical difficulties associated with the direct application of the quantum regression theorem in open quantum systems.Received: 6 September 2016, Accepted: 5 November 2016; Edited by: J. P. Paz; DOI: http://dx.doi.org/10.4279/PIP.080008Cite as: E A Gómez, J D Hernández-Rivero, H Vinck-Posada, Papers in Physics 8, 080008 (2016)This paper, by E A Gómez, J D Hernández-Rivero, H Vinck-Posada, is licensed under the Creative Commons Attribution License 3.0.

Very high thermoelectric figure of merit found in hybrid transition-metal-dichalcogenides

The search for thermoelectrics with higher figures of merit (ZT) will never stop due to the demand of heat harvesting. Single layer transition metal dichalcogenides (TMD), namely, MX2 (where M is a transition metal and X is a chalcogen), that have electronic band gaps are among the new materials that have been the focus of such research. Here, we investigate the thermoelectric transport properties of hybrid armchair-edged TMD nanoribbons, by using the nonequilibrium Green's function technique combined with the first principles and molecular dynamics methods. We find a ZT as high as 7.4 in hybrid MoS2/MoSe2 nanoribbons at 800 K, creating a new record for ZT. Moreover, the hybrid interfaces by substituting X atoms are more efficient than those by substituting M atoms to tune the ZT. The origin of such a high ZT of hybrid nanoribbons is the high density of the grain boundaries: the hybrid interfaces decrease thermal conductance drastically without a large penalty to electronic conductance.

Simultaneous observations of electromagnetically induced transparency (EIT) and absorption (EIA) in a multi-level V-type system of 87Rb and theoretical simulation of the observed spectra using a multi-mode approach.

We report here simultaneous experimental observation of Electromagnetically Induced Transparency (EIT) and Electromagnetically Induced Absorption (EIA) in a multi-level V-type system in D2 transition of Rb87, i.e., F=2→F' with a strong pump and a weak probe beam. We studied the probe spectrum by locking the probe beam to the transition F=2→F'=2 while the pump is scanned from F=2→F'. EIA is observed for the open transition (F=2→F'=2) whereas EIT is observed in the closed transition (F=2→F'=3). Sub natural line-width is observed for the EIA. To simulate the observed spectra theoretically, Liouville equation for the three-level V-type system is solved analytically with a multi-mode approach for the density matrix elements. We assumed both the pump and the probe beams can couple the excited states. A multi-mode approach for the coherence terms facilitates the study of all the frequency contributions due to the pump and the probe fields. Since the terms contain higher harmonics of the pump and the probe frequencies, we expressed them in Fourier transformed forms. To simulate the probe spectrum, we have solved inhomogeneous difference equations for the coherence terms using the Green's function technique and continued fraction theory. The experimental line-widths of the EIT and the EIA are compared with our theoretical model. Our system can be useful in optical switching applications as it can be precisely tuned to render the medium opaque and transparent simultaneously.

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier–Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge–Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.