Independent Particle Approximation Research Articles

SIMPLE code: Optical properties with optimal basis functions

We present SIMPLE, a code developed to calculate optical properties of metallic and insulating extended systems using the optimal basis method originally proposed by E.L. Shirley in 1996. Two different approaches for the evaluation of the complex dielectric function are implemented: (i) the independent-particle approximation considering both interband and intraband contributions for metals and (ii) the Bethe–Salpeter equation for insulators. Since, notably, the optimal basis set is systematically improvable, accurate results can be obtained at a strongly reduced computational cost. Moreover, the simplicity of the method allows for a straightforward use of the code; improvement of the optimal basis and thus the overall precision of the simulations is simply controlled by one (for metals) or two (for insulators) input thresholds. The code is extensively tested, in terms of verification and performance, on bulk silver for metals and on bulk silicon for insulators. Program summaryProgram Title:SIMPLEProgram Files doi:http://dx.doi.org/10.17632/99ps9dz428.1Licensing provisions: GNU General Public License v2Programming language: Fortran 95External routines: Quantum ESPRESSO distribution, BLAS, LAPACK, FFTW, MPI.Nature of problem: First-principles calculations of the optical properties of metals and insulators.Solution method: Shirley’s optimal basis for the complex dielectric function, at the independent-particle level for metals and by solving the Bethe–Salpeter equation for insulators.Restrictions: Norm-conserving pseudopotentials.

Optical properties of shortest-width zig-zag silicene nano-ribbons: Effects of local fields

Abstract We have computed from first principles the structural, magnetic and optical properties of zig-zag oriented silicene nanoribbons. The minimal width for structurally stable planar structure having zig-zag edges corresponds to a 4-chains ribbon. Its ground state presents reconstructed and spin polarized edges, coupled antiferromagnetically. For this state, and for the corresponding excited state with ferromagnetically coupled edges, we computed the optical absorption spectra within the independent particle approximation, including local field effect corrections, for light polarized in the directions parallel and perpendicular to the ribbon axis. For the “parallel” light polarization the inclusion of local fields effects is limited to a slight reduction of the intensity of the main peak in the infrared region, as well as that of some minor peaks in the visible-ultraviolet structure. Conversely, the computed optical spectrum for light polarized perpendicularly to the ribbon axis shows that the short-width zig-zag nanoribbons are basically transparent in the infrared and visible region, because of the effect of electronic confinement combined with local fields.

Relativistic Theory and Ab Initio Simulations of Electroweak Decay Spectra in Medium‐Heavy Nuclei and of Atomic and Molecular Electronic Structure

AbstractIn this work a novel theoretical and computational method for computing electroweak beta decay spectra of medium and heavy‐mass nuclei, as well as the electronic structure of atomic and molecular systems is developed. In particular, starting from the phenomenological electroweak interaction of the Standard Model (SM) of particles, a general expression of the beta decay rate was derived. Relativistic effects are taken into account by solving the many‐electron Dirac equation from first‐principles. Furthermore, an extension of this approach to include the nucleon‐nucleon interaction at the same level of theory of the electronic correlations has been devised. It is shown that post‐collisional effects, and to a lesser extent the electronic exchange and correlation, can modify significantly the cross‐section only at low energies (<10 keV), while nuclear correlations considerably affect the lineshape of both the absorption and emission spectra particularly in odd‐odd nuclear transitions, where the independent particle approximation, on which the nuclear shell model is framed, is more likely to fail. These findings demonstrate the importance of moving beyond the independent particle picture to obtain an accurate description of the experimental data by adding the many‐body correlations between the spectator and participator hadrons and leptons involved in the decay. The application of our approach to a number of test cases, such as the modeling of beta decay of 36Cl, 63Ni, 129I, 210Bi, 241Pu and of the electron capture of 138La3 + , leads to an extremely good agreement with the relevant experimental data. Finally, the extension of this method to atomic and molecular systems by calculating the electronic structures of 138La3 + and several isomers (MgCN, MgNC) and molecules (HMgCN, MgCNO, and BrCF3) relevant to astrophysical scenarios is presented. This method, which is capable to deal with both nucleonic and electronic degrees of freedom, has far‐reaching implications also in neutrino physics and nuclear astrophysics.

Theoretical Modeling of Electronic Excitations of Gas-Phase and Solvated TiO2 Nanoclusters and Nanoparticles of Interest in Photocatalysis.

The optical absorption spectra of (TiO2) n, nanoclusters ( n = 1-20) and nanoparticles ( n = 35, 84) have been calculated from the frequency-dependent dielectric function in the independent particle approximation under the framework of density functional theory. The PBE generalized gradient approach based functional, the so-called PBE+ U method and the PBE0 and PBEx hybrid functionals-containing 25% and 12.5% of nonlocal Fock exchange, respectively-have been used. The simulated spectra have been obtained in the gas phase and in water on previously PBE0 optimized atomic structures. The effect of the solvent has been accounted for by using an implicit water solvation model. For the smallest nanoclusters, the spectra show discrete peaks, whereas for the largest nanoclusters and for the nanoparticles they resemble a continuum absorption band. In the gas phase and for a given density functional, the onset of the absorption (optical gap, Ogap) remains relatively constant for all nanoparticle sizes although it increases with the percentage of nonlocal Fock exchange, as expected. For all tested functionals, the tendency of Ogap in water is very similar to that observed in the gas phase with an almost constant upshift. For comparison, the optical gap has also been calculated at the TD-DFT level with the PBEx functional in the gas phase and in water. Both approaches agree reasonably well although the TD-DFT gap values are lower than those derived from the dielectric-function. Overall, the position of the spectral maxima and the width of the spectra are relatively constant and independent of particle size which may have implications in the understanding of photocatalysis by TiO2.

Nonlinear optical responses of crystalline systems: Results from a velocity gauge analysis

In this work, the difficulties inherent to perturbative calculations in the velocity gauge are addressed. In particular, it is shown how calculations of nonlinear optical responses in the independent particle approximation can be done to any order and for any finite band model. The procedure and advantages of the velocity gauge in such calculations are described. The addition of a phenomenological relaxation parameter is also discussed. As an illustration, the nonlinear optical response of monolayer graphene is numerically calculated using the velocity gauge.

Ab initio calculation of the shift photocurrent by Wannier interpolation

We describe and implement a first-principles algorithm based on maximally-localized Wannier functions for calculating the shift-current response of piezoelectric crystals in the independent-particle approximation. The proposed algorithm presents several advantages over existing ones, including full gauge invariance, low computational cost, and a correct treatment of the optical matrix elements with nonlocal pseudopotentials. Band-truncation errors are avoided by a careful formulation of $k\cdot p$ perturbation theory within the subspace of wannierized bands. The needed ingredients are the matrix elements of the Hamiltonian and of the position operator in the Wannier basis, which are readily available at the end of the wannierization step. If the off-diagonal matrix elements of the position operator are discarded, our expressions reduce to the ones that have been used in recent tight-binding calculations of the shift current. We find that this `diagonal' approximation can introduce sizeable errors, highlighting the importance of carefully embedding the tight-binding model in real space for an accurate description of the charge transfer that gives rise to the shift current.

Optical properties of silicene, Si/Ag(111), and Si/Ag(110)

We present a state-of-the-art study of the optical properties of free-standing silicene and of single-layer Si 1D and 2D nanostructures supported on Ag(110) and Ag(111) substrates. Ab initio simulations of reflectance anisotropy spectroscopy (RAS) and surface differential reflectivity spectroscopy (SDRS) applied to the clean Ag surface and Si/Ag interfaces are compared with new measurements. For Si/Ag(110) we confirm a pentagonal nanoribbon geometry, strongly bonded to the substrate, and rule out competing zigzag chain and silicenelike models. For Si/Ag(111) we reproduce the main experimental features and isolate the optical signal of the epitaxial silicene overlayer. The absorption spectrum of a silicene sheet computed including excitonic and local field effects is found to be quite similar to that calculated within an independent particle approximation, and shows strong modifications when adsorbed on a Ag substrate. Important details of the computational approach are examined and the origins of the RAS and SDRS signals are explained in terms of the interface and substrate response functions. Our study does not find any evidence for Si adlayers that retain the properties of freestanding silicene.

Validity of Weyl fermion picture for transition metals monopnictides TaAs, TaP, NbAs, and NbP from ab initio studies

We investigate electronic and optical properties of the topological Weyl semimetals TaAs, TaP, NbAs and NbP crystallizing in bct geometry by means of the ab initio density functional theory with spin-orbit interaction within the independent-particle approximation. The small energetical overlap of Ta5d or Nb4d derived conduction and valence bands leads to electron and/or hole pockets near the Fermi energy at the 24 Weyl nodes. The nodes give rise to two-(three-)dimensional Dirac cones for the W1 (W2) Weyl type. The band dispersion and occupation near the Weyl nodes determine the infrared optical properties. They are dominated by interband transitions, which lead to a deviation from the expected constant values of the imaginary part of the dielectric function. The resulting polarization anisotropy is also visible in the real part of the optical conductivity, whose lineshape deviates from the expected linearity. The details of the Weyl nodes are discussed in relation to recent ARPES results for TaAs and NbP, and compared with measured optical spectra for TaAs. The spectral features of the anisotropic and tilted Weyl fermions are restricted to low excitation energies above absorption onsets due to the band occupation.

Second harmonic generation property of monolayer TMDCs and its potential application in producing terahertz radiation.

Second harmonic generation (SHG) properties in two-dimensional (2D) transition-metal dichalcogenides (TMDCs) have aroused great interest. However, until now SHG for TMDC monolayer alloys is seldom investigated. Meanwhile, there is considerable controversy over the static SHG coefficients of monolayer MoS2. The feasibility to produce terahertz (THz) radiation via SHG in pure and alloyed TMDCs has never been reported. We first calculate the SHG coefficients of monolayer MoS2, MoSe2, and MoS2(1-x)Se2x using the independent particle approximation plus scissors correction. We then simulate their THz absorption by applying density function perturbation theory plus the Lorentzian line and try to calculate their zero-frequency THz refractive index and birefringence. The physical property of MoS2(1-x)Se2x alloys is simulated by considering various combinations. Results indicate that monolayer MoS2, MoSe2, and MoS2(1-x)Se2x possess large static SHG coefficients and THz birefringence and display low absorption over broadband THz frequencies. Therefore, they have applications in producing THz radiation via SHG. This study demonstrates that THz radiation can be attained in a large number of monolayers and few-layers and will extend applications of 2D materials. Moreover, it is possible to identify the magnitude of static coefficients of single-layer MoS2 by measuring THz intensities.

Solving the Bethe-Salpeter equation for the second-harmonic generation in Zn chalcogenides

The influence of excitonic and local-field effects on the second-harmonic-generation spectrum of zinc-blende ZnS, ZnSe, and ZnTe is studied from first principles using the Bethe-Salpeter equation. The calculations are based on the theory of R. Leitsmann et al. [Phys. Rev. B 71, 195209 (2005)], which we extended to the low-frequency range. The dielectric function and the second-harmonic-generation spectrum have been obtained within the independent (quasi)particle approximation and within the Bethe-Salpeter approach. The calculations demonstrate that the linear and the nonlinear optical properties are similarly affected by excitonic and local-field effects. The computed spectra are furthermore compared with measurements and calculations within the time-dependent density-polarization functional theory (TD-DPFT) in the real-time framework. The present approach most commonly suggests stronger excitonic effects than observed in the real-time TD-DPFT calculations, while local-field corrections are comparably described. Although agreement is found between the Bethe-Salpeter spectra and measurements for the dielectric function, deviations from the experimental data are observed for second-harmonic generation.

Excitonic effects on the optical response of monolayer and bilayer graphene-like silicon carbide

The graphene-like silicon carbide (SiC) has attracted much attention recently owing to its potential application in optoelectric devices. In this work, we have theoretically investigated the excitonic effects on the dielectric constants [ε(ω)] of monolayer (ML-) and bilayer (BL-) SiC using the first principle calculations with solving the Bethe-Salpeter equation. The Tran-Blaha modified Becke-Johnson exchange potential combined with the Perdew and Wang correlation potential is used to overcome the underestimate of bandgap. Within the independent particle approximation, BL-SiC not only has the same intralayer π→π∗ transition in the transverse ε(ω) as ML-SiC but also has an interlayer π→π∗ transition in the longitudinal ε(ω). The excitonic effects dramatically change the absorption spectra of two polarization directions (transverse and longitudinal). For the transverse ε(ω), BL-SiC has a similar excitonic absorption profile to ML-SiC but shows a blue-shift relative to ML-SiC and an apparent decrease in the binding energy of bright exciton. For the longitudinal ε(ω), ML-SiC has a bright exciton with a large binding energy of 1.87eV related to the σ→π∗ transition band, and BL-SiC has a bright exciton with a small binding energy of 0.41eV related to the interlayer π→π∗ transition.

Synchrotron radiation induced X‐ray production cross sections of 66Dy at energies across its Li (i = 1–3) subshell absorption edges

The X‐ray production (XRP) cross sections for the 66Dy Lk (k = l, α, η, β2,6,7,15, β1,6, β1,3,4,6, β2,7,15, γ1,5, γ2,3) emission lines have been measured by tuning the incident synchrotron radiation at energies over the range 7.8–9.2 keV and ~10–370 eV above the respective Li (i = 1–3) absorption edges. These measurements aim to check the reliability of the independent particle approximation models used to generate the theoretical data sets of different physical parameters required to calculate the XRP cross sections and also investigate the influence of many body effects on the photoionization process. The measured values have been compared with 4 sets of XRP cross sections calculated using the Dirac–Fock model‐based X‐ray emission rates, 2 sets of the Li (i = 1–3) subshell photoionization cross sections deduced from the self‐consistent Dirac–Hartree–Fock model‐based values and the nonrelativistic Hartree–Fock–Slater model‐based values, and 2 sets of the fluorescence (ωi) and Coster–Kronig (fij) yields. The present measured Lγ2,3 (originating from decay of the L1 subshell vacancies) XRP cross sections are found to be significantly higher than different sets of theoretical values, whereas a good agreement is generally observed for the various other XRP cross sections and relative intensities.

Production and decay of K -shell hollow krypton in collisions with 52–197-MeV/u bare xenon ions

X-ray spectra of K-shell hollow krypton atoms produced in single collisions with 52 - 197 MeV/u Xe54+ ions are measured in a heavy-ion storage ring equipped with an internal gas-jet target. Energy shifts of the K{\alpha}_1,2^s, K{\alpha}_1,2^(h,s), and K\b{eta}_1,3^s transitions are obtained. Thus, the average number of the spectator L-vacancies presented during the x-ray emission is deduced. From the relative intensities of the K{\alpha}_1,2^s and K{\alpha}_1,2^(h,s) transitions, the ratio of K-shell hollow krypton to singly K-shell ionized atoms is determined to be 14 - 24%. In the considered collisions, the K-vacancies are mainly created by the direct ionization which cannot be calculated within the perturbation descriptions. The experimental results are compared with a relativistic coupled channel calculation performed within the independent particle approximation.

Photoelectron distribution of nonresonant two-photon ionization of neutral atoms

Photoelectron angular distributions following the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically. Using the independent particle approximation and relativistic second-order perturbation theory, the contributions of screening and relativistic effects to the photoelectron angular distribution are evaluated. A simple nonrelativistic expression is presented for the angle-differential cross section in dipole approximation for two-photon ionization by elliptically polarized photons, and its limitations are analyzed numerically. Moreover, we show that screening effects of the inactive electrons can significantly affect the photoelectron distributions and can also lead to a strong elliptical dichroism. Numerical results are resented for the case of two-photon K-shell ionization of neutral Ne, Ge, Xe, and U atoms.

Comment on “Gamma-ray spectra from low-energy positron annihilation processes in molecules”

In the article by Ma~\emph{et al.}~[Phys.~Rev.~A {\bf 94}, 052709 (2016)], $\gamma$-ray spectra for positron annihilation on molecules were calculated in the independent-particle approximation with the positron wavefunction set to unity. Based on comparisons with experimental data they concluded that inner valence electrons play a dominant role in positron annihilation. These conclusions are incorrect and resulted from fallacious analysis that ignored the known effect of the positron wavefunction on the spectra.

Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects

We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.

Modeled optical properties of SiGe and Si layers compared to spectroscopic ellipsometry measurements

The optical response of strained SiGe alloys, as well as thin Si layers, is analyzed using a sp3d5s∗ tight-binding model within the independent particle approximation. The theoretical results are compared to measurements obtained on samples with various Ge content and layer thicknesses. The dielectric function is extracted from spectroscopic ellipsometry allowing a separation of its real and imaginary parts. Theory and simulation show similar trends for the variation of the dielectric function of SiGe with varying Ge content. Variations are also well reproduced for thin Si layers with varying thickness and are attributed to quantum confinement.

Relativistic calculations of the nonresonant two-photon ionization of neutral atoms

The non-resonant two-photon one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the K-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section, for the case of U, for example, they reduce the total cross section by a factor of two. Moreover, we have found that the account for the screening effects of the remaining electrons leads to occurrence of an unexpected minimum in the total cross section at the total photon energies equal to the ionization threshold, for the case of Ne, for example, the cross section drops there by a factor of three.

Accurateab initiotight-binding Hamiltonians: Effective tools for electronic transport and optical spectroscopy from first principles

The calculations of electronic transport coefficients and optical properties require a very dense interpolation of the electronic band structure in reciprocal space that is computationally expensive and may have issues with band crossing and degeneracies. Capitalizing on a recently developed pseudo-atomic orbital projection technique, we exploit the exact tight-binding representation of the first principles electronic structure for the purposes of (1) providing an efficient strategy to explore the full band structure $E_n({\bf k})$, (2) computing the momentum operator differentiating directly the Hamiltonian, and (3) calculating the imaginary part of the dielectric function. This enables us to determine the Boltzmann transport coefficients and the optical properties within the independent particle approximation. In addition, the local nature of the tight-binding representation facilitates the calculation of the ballistic transport within the Landauer theory for systems with hundreds of atoms. In order to validate our approach we study the multi-valley band structure of CoSb$_3$ and a large core-shell nanowire using the ACBN0 functional. In CoSb$_3$ we point the many band minima contributing to the electronic transport that enhance the thermoelectric properties; for the core-shell nanowire we identify possible mechanisms for photo-current generation and justify the presence of protected transport channels in the wire.

Classical trajectory Monte Carlo model calculations for ionization of the uracil molecule by impact of heavy ions

The ionization of the uracil molecule induced by heavy-ion impact has been investigated using the classical trajectory Monte Carlo (CTMC) method. Assuming the validity of the independent-particle model approximation, the collision problem is solved by considering the three-body dynamics of the projectile, an active electron and the molecule core. The interaction of the molecule core with the other two particles is described by a multi-center potential built from screened atomic potentials. The cross section differential with respect to the energy and angle of the electrons ejected in the ionization process has been calculated for an impact of 3.5 MeV u−1 ions. Total electron emission cross sections (TCS) are presented for () and projectiles as a function of the impact energy in the range from 10 keV u−1 to 10 MeV u−1. The dependence of the TCS on the charge state of the projectile has been investigated for 2.5 MeV u−1 () and () ions. The results of the calculations are compared with available experimental data and the predictions of other theoretical models: the first Born approximation with correct boundary conditions (CB1), the continuum-distorted-wave–eikonal-initial-state approach (CDW-EIS), and the combined classical-trajectory Monte Carlo–classical over-the-barrier model (CTMC-COB).