Complex band structure calculations based on the overbridging boundary matching method without using Green's functions

Ab initio electron propagator methods are developed to study electronic properties of molecular systems with strong electron-electron and electron-phonon interactions. For the calculation of electron Green's functions we apply a canonical small polaron transformation that intrinsically contains strong electron-phonon effects. In the transformed Hamiltonian, the energy levels for the noninteracting particles are shifted down by the relaxation (solvation) energies. The Coulomb integrals are also renormalized by the electron-phonon interaction. For certain values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative which implies the attraction between two electrons. Within the small polaron transformation we develop a diagrammatic technique for the calculation of electron Green's function in which the electron-phonon interaction is already included into the multiple phonon correlation functions. Since the decoupling of the phonon correlation functions is impossible, and therefore, a Wick's theorem for such correlation functions is invalid, there is no Dyson equation for the electron Green's function. To find the electron Green's function, we use different approximations. One of them is a link-cluster approximation that includes diagonal transitions for the renormalized zeroth Green's function. In the linked-cluster approach the Dyson equation is derived in the most general case, where the self-energy operator is an arbitrary functional (not only in the Hartree-Fock approximation). It is shown that even a Hartree-Fock electron (hole) is not a particle any longer. It is a quasiparticle with a finite lifetime that depends on energy of particle and hole states in different ways. As a consequence of this, a standard description of a Hartree-Fock approximation in terms of wave functions becomes inappropriate in this problem. To challenge the linked-cluster approximation we develop a different approach: a sequential propagation approximation where scattering events occur only for sequential transitions. A self-consistent Hartree-Fock equation for a four-index Green's function matrix is derived. In conclusion, the proposed schemes can be considered for future method developments for quantum chemical calculations for large molecules with strong nonadiabatic effects, e-e correlated electron transfer reactions, and electron transport in molecular transport junctions.

Matrix Green's function solution of closed-form singularity for functionally graded and transversely isotropic materials under circular ring force vector

Generalized Bloch wave functions of bulk structures, which are composed of not only propagating waves but also decaying and growing evanescent waves, are known to be essential for defining the open boundary conditions in the calculations of the electronic surface states and scattering wave functions of surface and junction structures. Electronic complex band structures being derived from the generalized Bloch wave functions are also essential for studying bound states of the surface and junction structures, which do not appear in conventional band structures. We present a novel calculation method to obtain the generalized Bloch wave functions of periodic bulk structures by solving a generalized eigenvalue problem, whose dimension is drastically reduced in comparison with the conventional generalized eigenvalue problem derived by Fujimoto and Hirose [Phys. Rev. B 67, 195315 (2003)]. The generalized eigenvalue problem derived in this work is even mathematically equivalent to the conventional one, and, thus, we reduce computational cost for solving the eigenvalue problem considerably without any approximation and losing the strictness of the formulations. To exhibit the performance of the present method, we demonstrate practical calculations of electronic complex band structures and electron transport properties of Al and Cu nanoscale systems. Moreover, employing atom-structured electrodes and jellium-approximated ones for both of the Al and Si monatomic chains, we investigate how much the electron transport properties are unphysically affected by the jellium parts.

ABSTRACTWe present the mathematical and numerical theory for evanescent waves in subwavelength bandgap materials. We begin in the one‐dimensional case, whereby fully explicit formulas for the complex band structure, in terms of the capacitance matrix, are available. As an example, we show that the gap functions can be used to accurately predict the decay rate of the interface mode of a photonic analogue of the Su–Schrieffer–Heeger model. In two dimensions, we derive the bandgap Green's function and characterize the subwavelength gap functions via layer potential techniques. By generalizing existing lattice‐summation techniques, we illustrate our results numerically by computing the complex band structure in a variety of settings.

A simple computational method for internal polarized radiation fields of finite slab atmospheres

Considering both the gradient decay of the real disorder and the contact scattering, we investigate the electronic transport in quasi-one-dimensional nanowires by developing a decomposition elimination method for Green's function matrix. In the presence the contact scattering, the conductance oscillates with energy. For some energies of incident electrons, an abnormal enhancement is obtained in the average conductance due to the destroyed coherence by the introduction of much low disorder, showing that there appears a new conductance peak. In the absence of disorder gradient, the average conductance firstly decreases then increases with disorder strength, indicating that there exists a localization-delocalization transition. In the presence of linearly decaying disorder, the average conductance increases slightly in a strong disorder region. In the case of the Gaussian-type decaying disorder, the average conductance decreases exponentially and the localization-delocalization transition disappears, which is different from previous thereotical result. The results are helpful for the design and the application of quasi-one-dimensional nanowires device.

Near-field acoustical holography (NAH) requires the measurement of the pressure field over a closed surface in order to recover the normal velocity on a nearby concentric surface. It is impractical for large structure when the reconstruction of the field is required only on a partial structure surface. The method of superposition may be applied to reconstruct the field on a partial surface on a structure form measurements made on a nearby limited surface. According to the wave superposition method (WSM), the field on and near the measurement surface may be approximated by the field produced by virtual source points placed on a surface inside the structure. The source strengths are evaluated by applying boundary conditions on the measurement surface. Here, an iterative procedure is applied to extend the measurement surface in order to obtain better reconstruction precision. The algorithm requires the inversion of the Green's function matrix which may be ill-conditioned. Tikhonov regularization method is used to invert it, and the value of the regularization parameter is determined based on use of the L-curve criteria. A numerical simulation of two ball sound sources as an example to validate the results is used. The result of experiment shows the superiority and applicability of the data extrapolation based on patch-NAH.

The results of a first-principles calculation for the formation energy of a single vacancy in aluminum are reported. Solid-state scattering theory is modified to use localized Gaussian orbitals (instead of Wannier functions) and applied to evaluate the one-electron contribution. Energy bands and wavefunctions, obtained from a self-consistent LCGO band calculation, are used to evaluate the Green's function matrix. The defect potential consists of that due to the absence of a neutral atom, including the lattice relaxation. It is further made partially self-consistent by including the electronic dielectric function for screening.

A non-invasive, synthesizing array of "N" reciprocal transducers is driven by "N" linearly independent inputs for three-dimensional sound field specification at "N" locations either within, or on, an isotropic or anisotropic acoustic/elastodynamic medium. Towards these ends, the impulse response, or Dyadic Green's Function Matrix, characteristic of the medium is determined, and the desired sound field response at "N" locations either within, or on, the surface of the medium is specified. This results in a system of "N" equations, which can be solved to obtain the "N" linearly independent inputs required to create the "N" desired, three-dimensional sound field responses. This permits precise focusing and spatial manipulation of sound intensity, as well as amplitude control within a specific volume or region of convergence within, or on, the medium.

A novel version of the 2-D adaptive integral method (AIM), called circulant AIM, is presented. The method is suited particularly to cylindrical structures of a quasicircular cross section, such as the wall of a jet engine inlet. Unlike in standard AIM, the auxiliary grid, where the scatterer is embedded, is no longer Cartesian, but polar/cylindrical, resembling a spider's web. In this way, a much lower number of auxiliary unknowns are required, since only delta sources sufficiently close to the outer surface are utilized. Apart from significant savings in memory, the main advantage of this geometry is that the resulting Green's function matrix is not merely Toeplitz, but also circulant, leading to enhanced efficiency of the technique.

A structure having arbitrarily located conductor lines immersed in complex anisotropic layered media presents one with a very general guided wave problem. This problem is solved here by a rigorous formulation technique characterizing each layer by a 6 x 6 constitutive tensor and finding the appropriate Fourier transformed Green's function matrix G. From G a method of moments solution for the propagation characteristics follows including propagation constant eigenvalues and field eigenvectors at all spatial locations.

A computational scheme is described which simplifies many Green's-function calculations of energy-dependent quantities such as the density of states through a novel use of analytic properties. Calculations are performed at complex energies well above the real axis where the quantities of interest are slowly varying. Physical results are then obtained by analytically continuing Green's-function matrix elements back to real energies using an efficient numerical procedure based on Taylor-series expansions. The approach is simple, versatile, and particularly well suited for evaluating the complicated Brillouin-zone integrals which often appear in Green's-function calculations. In recent coherent-potential-approximation (CPA) calculations for ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Cd}}_{x}\mathrm{Te}$, the use of this technique cut the required computer time by about a factor of 3.

In protein electron transfer reaction rate calculations, the electronic Hamiltonian is apportioned into donor-acceptor (D-A) and protein bridge subspaces, and a two-state system is defined for the D-A subspace. Löwdin partitioning is used to perform the two-state reductions necessary to compute the tunneling matrix element between D and A sites. Here, a method of performing donor and acceptor state analysis for a non-orthogonal basis set in both the weak and strong electronic coupling regimes is developed. The electron tunneling current and coupling are obtained in terms of D-A symmetric and antisymmetric interatomic tunneling elements, and are then used to compare pathway models. These interatomic tunneling elements are both proportional to the Green's function elements of the isolated protein bridge. To facilitate a perturbative treatment of antisymmetric interatomic tunneling currents, we found a well-known expression for the D-A tunneling matrix element in terms of transformed Green's function matrix elements of the isolated protein bridge. Also, the relationship of the tunneling matrix element to BO pathways is discussed using the symmetric interatomic coupling. Finally, the definition of the average interatomic and atomic pathway coupling allows us obtain the quantum interference between interatomic tunneling pathways.

Evanescent Lamb waves in viscoelastic phononic metastrip

In this paper, we use a tight binding Hamiltonian with spin orbit coupling to study the real and complex band structures of relaxed and strained GaAs. A simple d orbital on-site energy shift coupled with appropriate scaling of the off-diagonal terms is found to correctly reproduce the band-edge shifts with strain. Four different ⟨100⟩ strain combinations, namely, uniaxial compressive, uniaxial tensile, biaxial compressive, and biaxial tensile strain are studied, revealing rich valence band structure and strong relative orientation dependent tunneling. It is found that complex bands are unable to provide unambiguous tunneling paths away from the Brillouin zone center. Tunneling current density distribution over the Brillouin zone is computed using non-equilibrium Green's function approach elucidating a physical picture of band to band tunneling.