Self-energy Matrix Research Articles

Time-dependent quantum transport: An efficient method based on Liouville-von-Neumann equation for single-electron density matrix

Basing on our hierarchical equations of motion for time-dependent quantum transport [X. Zheng, G. H. Chen, Y. Mo, S. K. Koo, H. Tian, C. Y. Yam, and Y. J. Yan, J. Chem. Phys. 133, 114101 (2010)], we develop an efficient and accurate numerical algorithm to solve the Liouville-von-Neumann equation. We solve the real-time evolution of the reduced single-electron density matrix at the tight-binding level. Calculations are carried out to simulate the transient current through a linear chain of atoms, with each represented by a single orbital. The self-energy matrix is expanded in terms of multiple Lorentzian functions, and the Fermi distribution function is evaluated via the Padè spectrum decomposition. This Lorentzian-Padè decomposition scheme is employed to simulate the transient current. With sufficient Lorentzian functions used to fit the self-energy matrices, we show that the lead spectral function and the dynamics response can be treated accurately. Compared to the conventional master equation approaches, our method is much more efficient as the computational time scales cubically with the system size and linearly with the simulation time. As a result, the simulations of the transient currents through systems containing up to one hundred of atoms have been carried out. As density functional theory is also an effective one-particle theory, the Lorentzian-Padè decomposition scheme developed here can be generalized for first-principles simulation of realistic systems.

SPIN TRANSPORT IN FRACTAL CONDUCTORS WITH THE RASHBA SPIN-ORBIT COUPLING

Spatial behavior of spin transport in a Sierpinski gasket fractal subject to the Rashba spin-orbital coupling is studied from two dimensions to a quasi-one dimensional arrangement. We represent two normal metal leads by a self-energy matrix, discretize the derived continuous Hamiltonian in the tight-binding approximation, and apply the Landauer–Keldysh formalism to the nonequilibrium transport. It is observed that the spin Hall effect present in the resultant distribution of spin density critically depends on the fractal structure and the shape of the thin film. The local spin density and transmission are numerically computed for both fractal and nonfractal thin films varying from a two dimensional square lattice into a quasi-one dimensional fractal shape. Spin filter effect is observed from the asymmetrical geometrical shape of Sierpinski triangle and pure spin current can be derived at appropriate conditions.

Consequences of theBABARand KLOEe+e−→π+π−data for the determination of model-dependentρ-ωmixing effects inΠρω(mρ2)and(g−2)μ

We update our analysis of $\ensuremath{\rho}$-$\ensuremath{\omega}$ mixing effects in the pion form factor to incorporate the recently published BABAR and KLOE ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ cross sections. Implications for $\ensuremath{\tau}$-decay-based standard model estimates of the leading order hadronic contribution to the muon anomalous magnetic moment, and for the extraction of the off-diagonal vector meson self-energy matrix element, ${\ensuremath{\Pi}}_{\ensuremath{\rho}\ensuremath{\omega}}({m}_{\ensuremath{\rho}}^{2})$, are discussed.

Cluster dynamical mean-field study of strongly correlated heterostructures: Correlation-induced reduction of proximity effect

We present a dynamical mean-field theory (DMFT) study of strongly correlated heterostructures. In contrast to previous DMFT work on multilayered systems, which was mainly based on the single-site approximation, we investigate the role of interplanar Coulomb correlations by using cellular DMFT. Accordingly, the self-energy matrix exhibits off-diagonal components in the layer index. As a model system we consider the single-band Hubbard model in a thin film geometry. The films can be either free standing or sandwiched between semi-infinite metallic leads. For isolated thin films, it is shown that the metal-insulator phase transition occurs either via a conventional mechanism, with a diverging imaginary part of the local self-energy, or via another one involving a discontinuous change of the real part of the off-diagonal self-energy. When the film is connected to metallic leads, the former phase transition disappears due to the normal-metal proximity effects, whereas the latter survives and significantly influences the electronic properties of the thin film. The leakage of metallic states into the Mott gap of the correlated film is greatly reduced compared to single-site DMFT calculations.

High-Order Element Effects of the Green's Function in Quantum Transport Simulation of Nanoscale Devices

High-order element (HOE) effects of the Green's function are studied by virtue of a comparative study between the recursive Green's function (RGF) method and the contact block reduction approach in double-gate metal-oxide-semiconductor field-effect transistor simulations. In general, quantum-mechanical simulations of 2-D and 3-D nanoscale devices are very computationally challenging. An efficient and widely used approach for the multidimensional problems is the RGF method. As the tridiagonal or block tridiagonal property of a self-energy matrix is exploited in the RGF method, the HOEs of the gate contact self-energy matrix are often omitted. This study on the HOE effects offers a good physical insight as well as provides a necessary measure on the applicability of the RGF method. Specifically, effects on gate current, electron density, and current density are investigated.

Many-body theory of electronic transport in single-molecule heterojunctions

A many-body theory of molecular junction transport based on nonequilibrium Green's functions is developed, which treats coherent quantum effects and Coulomb interactions on an equal footing. The central quantity of the many-body theory is the Coulomb self-energy matrix ${\ensuremath{\Sigma}}_{C}$ of the junction. ${\ensuremath{\Sigma}}_{C}$ is evaluated exactly in the sequential-tunneling limit, and the correction due to finite tunneling width is evaluated self-consistently using a conserving approximation based on diagrammatic perturbation theory on the Keldysh contour. Our approach reproduces the key features of both the Coulomb blockade and coherent transport regimes simultaneously in a single unified transport theory. As a first application of our theory, we have calculated the thermoelectric power and differential conductance spectrum of a benzenedithiol-gold junction using a semiempirical $\ensuremath{\pi}$-electron Hamiltonian that accurately describes the full spectrum of electronic excitations of the molecule up to 8--10 eV.

Localized exchange-correlation potential from second-order self-energy for accurate Kohn-Sham energy gap

A local Kohn-Sham (KS) exchange-correlation potential is derived by localizing the second-order self-energy operator, using approximations to the linear response Sham-Schlüter equation. Thanks to the use of the resolution-of-identity technique for the calculation of the self-energy matrix elements, the method is very efficient and can be applied to large systems. The authors investigate the KS energy gaps and lowest excitation energies of atoms and small- and medium-size molecules. Reference KS energy gaps (from accurate densities) of atoms and small molecules can be reproduced with great accuracy. For larger systems they found that the KS energy gap is smaller than the one obtained from the local-density approximation, showing the importance of an ab initio correlation in the Kohn-Sham potential.

Spin-fluctuation mechanism of superconductivity in cuprates

The theory of superconductivity within the t-J model, as relevant for cuprates, is developed. It is based on the equations of motion for projected fermionic operators and the mode-coupling approximation for the self-energy matrix. The dynamical spin susceptibility at various doping is considered as an input, extracted from experiments. The analysis shows that the superconductivity onset is dominated by the spin-fluctuation contribution. We show that T_c is limited by the spin-fluctuation scale $\Gamma$ and shows a pronounced dependence on the next-nearest-neighbor hopping t'. The latter can offer an explanation for the variation of T_c among different families of cuprates.

Nonlinear sigma model for a condensate composed of fermionic atoms

A nonlinear sigma model is derived for the time development of a Bose–Einstein condensate composed of fermionic atoms. Spontaneous symmetry breaking of a Sp ( 2 ) symmetry in a coherent state path integral with anticommuting fields yields Goldstone bosons in a Sp ( 2 ) ⧹ U ( 2 ) coset space. After a Hubbard–Stratonovich transformation from the anticommuting fields to a local self-energy matrix with anomalous terms, the assumed short-ranged attractive interaction reduces this symmetry to a SO ( 4 ) ⧹ U ( 2 ) coset space with only one complex Goldstone field for the singlet pairs of fermions. This bosonic field for the anomalous term of fermions is separated in a gradient expansion from the density terms. The U ( 2 ) invariant density terms are considered as a background field or unchanged interacting Fermi sea in the spontaneous symmetry breaking of the SO ( 4 ) invariant action and appear as coefficients of correlation functions in the nonlinear sigma model for the Goldstone boson. The time development of the condensate composed of fermionic atoms results in a modified Sine–Gordon equation.

Fast electron relaxation times in coupled double quantum well structures

We study the electron–electron interaction induced energy-dependent inelastic carrier relaxation processes of fast electrons and their corresponding lifetimes in doped semiconductor coupled double quantum well nanostructures within the two subband approximation at zero temperature. The lifetime of these electrons is obtained and studied by using many-body theory based upon generalized multisubband GW approximation. The imaginary part of the full self-energy matrix is calculated by expanding in the dynamically RPA screened Coulomb interaction. We also comment on the effects of structural asymmetry and tunneling between the layers.

Carrier relaxation due to electron-electron interaction in coupled double quantum well structures

We calculate the electron-electron interaction induced energy-dependent inelastic carrier relaxation rate in doped semiconductor coupled double quantum well nanostructures within the two subband approximation at zero temperature. In particular, we calculate, using many-body theory, the imaginary part of the full self-energy matrix by expanding in the dynamically RPA screened Coulomb interaction, obtaining the intrasubband and intersubband electron relaxation rates in the ground and excited subbands as a function of electron energy. We separate out the single particle and the collective excitation contributions, and comment on the effects of structural asymmetry in the quantum well on the relaxation rate. Effects of dynamical screening and Fermi statistics are automatically included in our many body formalism rather than being incorporated in an ad-hoc manner as one must do in the Boltzman theory.

A brief comparison between two programs that compute the static conductance of a disordered two-dimensional tight-binding system

There are two programs in the CPC program library that compute the static conductance of a disordered two-dimensional cluster described by a tight-binding Hamiltonian. The older program uses the Landauer scheme to get the conductance from the transmittance of a cluster attached to two semi-infinite chains that play the role of physical leads. The second program directly uses the Kubo formula to get the conductance of a similar cluster connected to leads of arbitrary width. In both cases, the local Green function should be calculated, but while the first method uses the idea of recursion and implements a set of subroutines to get the desired matrix elements of the resolvent, the second method employs LAPACK subroutines to propagate the self-energy matrix from one side of the cluster to the other. At the end both methods deliver the same numerical answer, with a comparable high precision but at quite different computing speeds. The newer method is typically one order of magnitude quicker thanks to modern methods in linear algebra when just one system is solved, but recursion is advantageous for solving the same systems for several Fermi energies because in this case the slow part of the calculation is done only once.

A nondiagonal, renormalized extension of partial third-order quasiparticle theory: Comparisons for closed-shell ionization energies

Valence ionization energies of a set closed-shell molecules calculated in a nondiagonal, renormalized approximation of the electron propagator have an average absolute error of 0.17 eV. This procedure extends the partial third order, quasiparticle approximation of J. Chem. Phys. 104, 7599 (1996) that has proven successful in many applications. Elements of the self-energy matrix include all second-order and many higher-order terms. Because of its fifth power dependence on basis set size and its independence from electron repulsion integrals with four virtual orbital indices, this method has considerable promise for large molecules. Formal and computational comparisons with renormalized electron propagator techniques that are complete through third-order illustrate the advantages of this procedure.

Strong-coupling theory for the spin-phonon model

We present a strong-coupling approach to the spin-phonon model with a cubic spectral density, which relies on a matrix representation for the reduced time evolution operator on the four-dimensional space of pseudospins. The $4\ifmmode\times\else\texttimes\fi{}4$ self-energy matrix $\ensuremath{\Sigma}$ is written as an infinite series in powers of bath fluctuation operators, and the lowest-order approximation is evaluated explicitly. The diagonal element ${\ensuremath{\Sigma}}_{\mathrm{zz}}$ corresponds to the result of the noninteracting blip approximation (NIBA); retaining the full matrix is equivalent to taking into account certain blip-blip interactions. Contrary to NIBA, this approach agrees with a rigorous result for the quadratic term of the rate. As a main result, we find a crossover to incoherent motion at a temperature ${T}^{*}$, which is compared to previous theoretical work and discussed in view of experimental data for various two-level tunneling systems.

Resonance formation of hydrogenic levels in front of metal surfaces

The electronic self-energy of hydrogenic ions interacting with a jellium metal surface is studied within the fixed-ion approximation. A model framework is introduced that allows for the efficient computation of the complex (non-Hermitian) self-energy matrix in a large space of (bound) hydrogenic states. For the specific case of protons interacting with an aluminum surface, resonance energies and widths of dressed ionic states are obtained by diagonalizing the self-energy matrix. The hybridization properties of the dressed ionic states are analyzed. The self-energy of individual dressed states is found to converge rapidly with increasing dimension of the space of unperturbed hydrogen states. The resonance energies are compared to (1) energies obtained by diagonalizing only the direct couplings among the hydrogen states and (2) the real part of the diabatic (diagonal) self-energy. This comparison demonstrates the pronounced effect that indirect couplings between hydrogen states via conduction band states have on the resonance energies at intermediate and small ion-surface distances. Our results for incident protons are confronted with the results of other (perturbative and nonperturbative) calculations of level shifts and widths in proton-surface interactions. Although we use a simplified electronic potential, we find good agreement with calculations employing more refined potentials.

QED symmetries in real-time thermal field theory

We study the discrete and gauge symmetries of quantum electrodynamics at finite temperature within the real-time formalism. The gauge invariance of the complete generating functional leads to the finite temperature Ward identities. These Ward identities relate the eight vertex functions to the elements of the self-energy matrix. Combining the relations obtained from the ${Z}_{2}$ and the gauge symmetries of the theory we find that only one out of eight longitudinal vertex functions is independent. As a consequence of the Ward identities, it is shown that some elements of the vertex function are singular when the photon momentum goes to zero.

One-particle dynamics in the Hubbard model at half-filling

The one-particle Green function for the 2d Hubbard model at half-filling and zero temperature is considered. By use of projection technique we derive equations of motion for the Green functions related to the four Hubbard operators c ̂ kσ α and c ̂ kσ α . Here, the index α = 1, 2indicates the two sublattices of the antiferromagnetic phase. The operator c ̂ kσ α creates a hole on sublattice α at singly occupied sites. Similarly, c ̂ kσ α annihilates an electron at doubly occupied sites. The self-energy matrix is decoupled and a self-consisten scheme for the Green functions is found. This scheme can be considered a generalization of one derived recently for the t- J model. For the hole band, described by the operators c ̂ kσ α , our result for U⪢ t shows strong coupling of the hole to spin excitations, similar to that found for the t- j model, with the additional feature that propagation of up-spin holes on the down sublattice is taken into account. For decreasing U the gap decreases roughly proportional to the staggered magnetization m. For U → 0, where m vanishes, we find the correct limit of uncorrelated electrons.

Partial third-order quasiparticle theory: Comparisons for closed-shell ionization energies and an application to the Borazine photoelectron spectrum

Valence ionization energies of a set closed-shell molecules calculated in a partial third-order (P3) quasiparticle approximation of the electron propagator have an average absolute error of 0.19 eV. Diagonal elements of the self-energy matrix include all second-order and some third-order self-energy diagrams. Because of its fifth power dependence on basis set size and its independence from electron repulsion integrals with four virtual indices, this method has considerable potential for large molecules. Formal and computational comparisons with other electron propagator techniques illustrate the advantages of the P3 procedure. Additional applications to benzene and borazine display the efficacy of the P3 propagator in assigning photoelectron spectra. In the borazine spectrum, 2E′ and 2A2′ final states are responsible for an observed feature at 14.76 eV. Another peak at 17.47 eV is assigned to a 2E′ final state.

Remarks on the Coulomb and covariant gauges in finite temperature QED

We compare the use of the Coulomb gauge in finite temperature QED with a recently proposed prescription for covariant gauges, in which only the transverse photon degrees of freedom are thermalized. Using the Landau rule as a guide, we clarify the relation between the retarded electron self-energy and the elements of the self-energy matrix in the real-time formulation of Finite Temperature Field Theory. The general results are illustrated by means of the one-loop expressions for the electron self-energy in a QED plasma.

Resonant 3d, 3p and 3s Photoemission in Transition Metal Oxides Predicted at 2p Threshold

We present calculated 3 d , 3 p and 3 s resonant photoemission (RPE) spectra in the transition metal (TM) compounds CuO, NiO, CoO, FeO, MnO and TiO 2 at TM 2 p core threshold on the basis of a cluster model. Our model includes the intraatomic multipole electron-electron interactions and the hybridization between transition metal ions and ligand. The imaginary part of the self-energy matrix of the intermediate state is calculated by taking into account the 2 p 3 d 3 d , 2 p 3 d 3 p , 2 p 3 d 3 s and 2 p 3 p 3 p Coster-Kronig decay, which guarantees a sum rule between the integrated RPE spectra and absorption spectra. The dependence of RPE on the incident photon energy tuned to various multiplet structures of TM 2 p absorption spectra is shown to be useful to identify the second order optical process, which is argued to include much Auger decay component. It is also shown, by a comparison with experiment, that the present 3 d RPE contributes to a removal of discrepancies of estimated parameter values among ...