Independent Particle Approximation Research Articles

From Bulk to one-dimensional MoS2 nanochains: evolution of electronic, mechanical, and optical properties

We theoretically investigate the stability of a MoS2 nanochain, reporting its electronic, mechanical, and optical properties. The nanochain presents a semiconductor structure with a minute band gap of 67m eV compared to the larger gap bulk and monolayer structures. It is more malleable, enduring a maximum compressive (tensile) strain of 6% (6.5%). It is dynamically stable, showing no negative frequencies along its Brillouin zone (BZ) path. The nanochain is thermally stable at 300K, making it possible to synthesize as a freestanding structure. The optical properties of the bulk, monolayer, and 1D MoS2 materials are evaluated using the time-dependent density functional perturbation theory (TDDFPT) and compared to those determined via the independent particle approximation (IPA). Along the nanochain’s periodic x direction, the reflectivity retains a maximum value of ∼68% in the infrared (IR) region. Furthermore, its optical conductivity also exhibits a peak within the IR regime. These two features make such nanochains suitable as coating materials in applications involving infrared radiation or can even be exploited as conductive substrates in near-IR devices.

Limitations of mean-field approximations in describing shift-current and injection-current in materials

We theoretically and computationally investigate bulk photovoltaic effects, with a specific focus on shift-current and injection-current. Initially, we perform a numerical analysis of the direct current (dc) induced by a laser pulse with a one-dimensional model, utilizing mean-field theories such as time-dependent Hartree–Fock and time-dependent Hartree methods. Our numerical results, obtained with mean-field theories, reveal that the dc component of the current, as a second-order nonlinear effect, exists even after irradiation with linearly polarized light as a second-order nonlinear effect, indicating the generation of injection-current. Conversely, when we employ the independent-particle approximation, no injection-current is generated by linearly polarized light. To develop the microscopic understanding of injection-current within the mean-field approximation, we further analyze the dc component of the current with the perturbation theory, employing the mean-field approximations, the independent-particle approximation, and the exact solution of the many-body Schrödinger equation. The perturbation analysis clarifies that the injection-current induced by linearly polarized light under the mean-field approximations is an artifact caused by population imbalance, created through quantum interference from unphysical self-excitation pathways. Therefore, investigation of many-body effects on the bulk photovoltaic effects have to be carefully conducted in mean-field schemes due to potential contamination by unphysical dc current. Additionally, we perform the first-principles electron dynamics calculation for BaTiO3 based on the time-dependent density functional theory, and we confirm that the above findings from the one-dimensional model calculation and the perturbation analysis apply to realistic systems. Published by the American Physical Society 2024

Energy and Z dependence of low velocity Nq+ ion induced M X-ray relative intensities for some heavy elements

The intensity ratios, IMk/IMn (exp)(k = ξ, γ, m1; n = total, αβ), for some heavy elements, 70Yb, 79Au, 81Tl, 82Pb and 83Bi induced by 1000 keV−1750 keV Nq+ (q = 4, 5) ions have been measured in order to investigate their dependence on the projectile energy and atomic number of the respective target elements. The measured intensity ratios have been compared with two sets of values calculated using the Mj (j = 1–5) sub-shell ionization cross sections based on the ECPSSR-UA model, the X-ray emission rates based on the Dirac-Hartree Slater (DHS) model, two sets of the fluorescence and Coster-Kronig yields based on the DHS model and those evaluated by McGuire employing non-relativistic Hartree-Slater model. Significant differences have been observed between the present measured IMk/IMαβ (exp) (k = ξ, γ, m1) intensity ratios and those calculated using independent particle approximation (IPA) models based single atomic vacancy state physical parameters.

Unveiling the Electronic Structure of SnS for Photocatalytic Applications: A DFT Approach†

AbstractPhotocatalytic materials are of great scientific interest due to their potential applications in sustainable energy sources. Band gap and optical absorption of the materials are two core characteristics for photocatalysis that eventually depend on electronic structure. In order to accurately compute (predict) the electronic‐scale properties of a crystalline solid using first principles calculations, which might be costly to measure experimentally, large‐scale atomic level calculation frameworks have been made possible through the use of density functional theory (DFT). We have used DFT with many body perturbation theory (MBPT) by solving the bethe‐salpeter equation (BSE) to priorly predict the properties of bulk tin sulfide (SnS) as it meets the necessary requirements for photocatalytic applications. We fixed the DFT band gap underestimation by including the Hubbard parameter (U) and used projector augmented wave pseudo‐potentials with generalized‐gradient approximation (GGA) to calculate the electronic and optical properties of SnS. Optical properties were computed using independent particle approximation (IPA) and BSE with DFT+U wave functions. Our theoretical results align with experimental data for this material, demonstrating the potential for further research in validating experimental results with theoretical approximations and empirical relations.

Black Phosphorene/MoS2 van der Waals heterostructure: Electronic and optical properties

In this study, we use density functional theory to calculate the optical and electronic properties of a black-phosphorene/MoS2 stack. We have considered different exchange–correlation functionals to account for the effects of van der Waals interaction and examined the impact of stacking order/layers alignment on the opto-electronic properties. Our findings reveal that the heterostructure exhibits a reduction in band gap and a modification of optical properties compared to single monolayers. The optical response was evaluated using an independent particle approximation to get the dielectric function’s imaginary part, which showed a strong absorption peak in the visible and ultraviolet regions. This feature could be helpful for optoelectronic applications. Nonetheless, the stacking order has a negligible effect on the electronic and optical properties of the BP/MoS2 bilayer.

On the excitonic effects of the 1T and 1O[formula omitted] phases of PdS2, PdSe2, and PdSSe monolayers

We report the excitonic effects in the 1T and 1OT phases of PdS2, PdSe2, and PdSSe monolayers. Using fully relativistic norm-conserving non-local PBE pseudopotentials and including the spin–orbit (SOC) coupling, the 1T geometries are indirect band gap semiconductors; conversely, the 1OT structures are semimetallic. The band gaps were corrected using the HSE06 hybrid functional, making all structures semiconductors. Maximally localized Wannier functions were utilized to fit the bands of all six structures. The excitonic band structures were obtained using the Bethe–Salpeter equation (BSE), and the absorption coefficients were estimated at both the BSE and the independent particle approximation (IPA) levels. While the 1OT monolayers are more inclined to absorb light polarized in the y-direction, the 1T structures absorb light equally, independent of the polarization direction. We perceive that the 1T phase is the most promising candidate for photovoltaic devices; in particular, the 1T PdSSe system possesses a maximum power conversion efficiency (PCE) of 29.31% if light trapping techniques are used to enhance absorbance. Amongst the 1OT materials, PdS2 features the highest PCE of 8.38%. Our results constitute the first step to encourage experimental studies towards the fabrication of Pd-based regular and Janus transition metal dichalcogenides photoabsorbers and give hints of how to increase the PCE of such materials.

Mean-field approximation of the Fermi–Hubbard model expressed in a many-body basis

The effective independent-particle (mean-field) approximation of the Fermi–Hubbard Hamiltonian is described in a many-body basis to develop a formal comparison with the exact diagonalization of the full Fermi–Hubbard model using small atomic chain as test systems. This allows for the development of an intuitive understanding of the shortcomings of the mean-field approximation and how critical correlation effects are missed in this popular approach. The description in the many-body basis highlights a potential ambiguity related to the definition of the density of states. Specifically, satellite peaks are shown to emerge in the mean-field approximation, in departure from the common belief that they characterize correlation effects. The scheme emphasizes the importance of correlation and how different many-body corrections can improve the mean-field description. The pedagogical treatment is expected to make it possible for researchers to acquire an improved understanding of many-body effects as found in various areas related to the electronic properties of molecules and solids.

Investigating the Linear Response Function under Approximations Following the Coupled-Perturbed Approach for Atoms and Molecules.

The linear response kernel also referred to as linear response function (LRF) in the framework of conceptual density functional theory has gained tremendous success in time-dependent density functional theory. Comparatively less attention has been devoted to the LRF from a chemical reactivity perspective in its time- or frequency-independent context, although it has recently been used to qualitatively describe electron delocalization, (anti-)aromaticity, inductive and mesomeric effects, etc. Despite these successes, which were obtained by approximating the LRF using the independent particle approximation deriving from a coupled-perturbed Kohn-Sham computation, the robustness of this LRF approach needs to be assessed. In this work, we compute the LRF at four levels of approximation (independent particle approximation, random phase approximation, Hartree-Fock approximation, and the (exact) DFT (density functional theory) expression) using functionals from the first four rungs of Jacob's ladder of exchange-correlation energy functionals. To scrutinize the impact of these approximations, new visualization strategies are discussed and systematized. The overall conclusion is that the independent particle approximation yields qualitatively correct results (ergo previous conceptual applications of the LRF are trustworthy), but for quantitative results, LRF expressions including coulomb and exchange(-correlation) terms should be included. With respect to functionals, density-gradient contributions to the exchange-correlation kernel are less than 10% and may be omitted safely where that is preferable computationally.

Multipole theory of optical spatial dispersion in crystals

Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of electromagnetism, where the coupling to light is treated semiclassically beyond the electric-dipole approximation. That theory has two shortcomings: it is limited to bounded systems, and its building blocks -the multipole transition moments- are origin dependent. In this work, we recast the multipole theory in a translationally-invariant form that remains valid for crystals. Working in the independent-particle approximation, we introduce "intrinsic" multipole transition moments that are origin independent and transform covariantly under gauge transformations of the Bloch eigenstates. Electric-dipole transitions are given by the interband Berry connection, while magnetic-dipole and electric-quadrupole transitions are described by matrix generalizations of the intrinsic magnetic moment and quantum metric. In addition to multipole-like terms, the response of crystals at first order in the wavevector of light contains band-dispersion terms that have no counterpart in molecular theories. The full response is broken down into magnetoelectric and quadrupolar parts, which can be isolated in the static limit where electric and magnetic fields become decoupled. The rotatory-strength sum rule for crystals is found to be equivalent to the topological constraint for a vanishing chiral magnetic effect in equilibrium, and the formalism is validated by numerical tight-binding calculations.

Effects of Opposite Atoms on Electronic Structure and Optical Absorption of Two‐Dimensional Hexagonal Boron Nitride

AbstractThe first‐principles many‐body GW and Bethe–Salpeter equation (BSE) calculations on the 2D hexagonal boron nitride (2D‐hBN) to explore the effects of opposite atoms on the electronic structure and linear one‐photon absorption (OPA) are performed. Five AA‐ and AB‐stacked bilayer and eight AAB‐stacked trilayer structures are considered. The AAB‐stacked trilayer hBN (TL‐BN) structures are constructed by mixing the AA‐ and AB‐stacked bilayer hBN (BL‐BN). It is shown that the GW approximation gives rise to different types (i.e., indirect or direct) of fundamental bandgaps from the independent particle approximation for all structures except those dominated by the B–B opposite. The stacking modes dominated by the B–B opposite have a direct fundamental bandgap in both approximations. The OPA spectra are calculated by solving the BSE combined with the GW quasi‐particle correction. The binding energy and Davydov splitting of excitons of TL‐BN strongly depend on the opposite atoms and are related to the role of the stacking BL‐BN substructure. Finally, taking the six‐layer and below AB‐stacked structures as examples, it is shown that the B–B opposite unit is helpful in constructing the turbostratic‐phase‐like stacking structures with a direct fundamental bandgap which are more suitable for optoelectronic applications.

Calculation of Atomic Scattering Factor For X-ray in Copper

In this paper the atomic scattering factor f( has been calculated for x-ray in copper using Wave function involves The independent particle approximation for the values , The physical importance of this factor appears in its relation with the several important atomic properties such as, the coherent scattering intensities, the total scattering, the incoherent scattering function, the cross section for coherent, incoherent scattering, the differential of electrons scattering from atom and the geometrical structure factor. There was difference of 23% between the values has been found and the values has been measured for atomic scattering factor.

Optical activity of solids from first principles

Within the framework of independent particle approximation, the optical activity tensor of solids is formulated as from different contributions: the magnetic dipole, electric quadrupole, and band dispersion terms. The first two terms have similar counterparts in the theory of finite systems, while the last term is unique for crystals. The magnetic dipole and electric quadrupole transition moments are calculated with a sum-over-states formulation. We apply the formulation to calculate and analyze the optical rotation of elemental tellurium and the circular dichroism of $(6,4)$ carbon nanotube. Decomposed optical activity into different contributions are discussed. The calculated spectra agree well with experiments. As a showcase of achiral crystals, we calculate the optical activity of wurtzite GaN.

First-principles study of the bandgap renormalization and optical property of β-LiGaO2

The β-LiGaO2 with an orthorhombic wurtzite-derived structure is a candidate ultrawide direct-bandgap semiconductor. In this work, using the non-adiabatic Allen–Heine–Cardona approach, we investigate the bandgap renormalization arising from electron–phonon coupling. We find a sizable zero-point motion correction of –0.362 eV to the gap at Γ, which is dominated by the contributions of long-wavelength longitudinal optical phonons. The bandgap of β-LiGaO2 decreases monotonically with increasing temperature. We investigate the optical spectra by comparing the model Bethe–Salpether equation method with the independent-particle approximation. The calculated optical spectra including electron–hole interactions exhibit strong excitonic effects, in qualitative agreement with the experiment. The contributing interband transitions and the binding energy for the excitonic states are analyzed.

Third-order optical nonlinearity of one-dimensional Dirac fermions

The optical nonlinearity of Dirac fermions in two and three dimensions show unique properties determined by analytic expressions in the independent particle approximation, which promotes their host materials as potential candidates for providing optical nonlinear functionalities. In this work we theoretically study the third-order optical nonlinearity for one-dimensional Dirac fermions and obtain analytical expressions for third-order optical conductivities at general light frequencies. The conductivity includes many resonant peaks induced by the resonant optical transitions associated with intraband motion as well as one-, two-, and three-photon interband processes. The conductivities for field-induced second harmonic generation and third harmonic generation are discussed in detail. To connect with real materials, we choose armchair graphene nanoribbons, which host one-dimensional Dirac fermions for its low energy electronic excitation, and our analytical expressions are applied to get the third-order conductivity for harmonic generations with different ribbon width. By comparing with numerical results evaluated from a full band structure in a tight binding model, the analytic and numerical results agree pretty well for photon energy below 2.5 eV.

Comparison of Electron Capture Rates in the N = 50 Region using 1D Simulations of Core-collapse Supernovae

Recent studies have highlighted the sensitivity of core-collapse supernovae (CCSNe) models to electron-capture (EC) rates on neutron-rich nuclei near the N = 50 closed-shell region. In this work, we perform a large suite of one-dimensional CCSN simulations for 200 stellar progenitors using recently updated EC rates in this region. For comparison, we repeat the simulations using two previous implementations of EC rates: a microphysical library with parametrized N = 50 rates (LMP), and an older independent-particle approximation (IPA). We follow the simulations through shock revival up to several seconds post-bounce, and show that the EC rates produce a consistent imprint on CCSN properties, often surpassing the role of the progenitor itself. Notable impacts include the timescale of core collapse, the electron fraction and mass of the inner core at bounce, the accretion rate through the shock, the success or failure of revival, and the properties of the central compact remnant. We also compare the observable neutrino signal of the neutronization burst in a DUNE-like detector, and find consistent impacts on the counts and mean energies. Overall, the updated rates result in properties that are intermediate between LMP and IPA, and yet slightly more favorable to explosion than both.

Ab initio calculation of two-photon absorption in semiconductors

A theoretical derivation of two-photon absorption (2PA) from semiconductors, based on the length gauge analysis and the electron density operator, is formulated; the intraband ${\mathbit{r}}_{i}$ part and the interband ${\mathbit{r}}_{e}$ part of the position operator $\mathbit{r}$ are properly accounted for. Within the independent-particle approximation, the nonlinear third-order susceptibility tensor ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ and the two-photon absorption coefficient are calculated, including the scissors correction needed to correct the well-known underestimation of the local-density-approximation band gap. Using time-reversal symmetry, it is shown that the expression for ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ is finite at $\ensuremath{\omega}=0$, avoiding nonphysical divergences presented in previous calculations when $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Ab initio band structure calculations using different pseudopotential schemes that include spin-orbit coupling are used to calculate the 2PA for several semiconductors, and the calculations are compared with available experimental results for photon energies that are below the optical band gap.

Optical properties and simulated x-ray near edge spectra for Y2O2S and Er doped Y2O2S

The electronic and optical properties of Y2O2S and its Er+3 doped counterparts at various concentrations are analyzed using density functional theory (DFT) and simulated x-ray near edge (XANES) spectra. Our simulations are complemented by absorption experiments, which show Y2O2S:Er+3 light emissions in the visible and near infrared. These emissions correspond to Er f–f intraband transitions. We use DFT and DFT+U to calculate the band structure of the Y2O2S and its Er+3 doped counterparts, whereas optical properties are calculated using the independent particle approximation (IPA). The host Y2O2S optical properties are also calculated using the random phase approximation (RPA) and the many-body GW0 approximation. Our IPA calculations on the Y2O2S:Er+3 reveal transitions in the energy region of the bandgap, which are absent in the host spectrum. These are assigned to Er f–f intraband transitions in the visible and near infrared, by applying a rigid energy shift. Moreover, XANES calculations at the Er M5-edge reveal a pre-edge broad shoulder in the proximity of the Er 4f band, which is also supportive of the f–f intraband transitions.

Power spectrum of relativistic heliumlike ions strongly coupled to two coherent light fields

Resonance fluorescence occurs when an atom is irradiated by a continuous monochromatic field. We analyze a ladder-type heliumlike highly charged ion, strongly coupled to two coherent light fields. The independent-particle approximation, where electron–electron correlations are neglected, works very well for few-electron ions when the nuclear charge Z is greater than 50. In order to treat heliumlike systems, one decomposes the corresponding matrix elements into hydrogenlike matrix elements using the independent-particle approximation. To calculate the hydrogenlike matrix elements, we consider that energy states are described fully relativistically.

Polarization effects in the total rate of biharmonic ω+3ω ionization of atoms

The total ionization rate of biharmonic ($\ensuremath{\omega}+3\ensuremath{\omega}$) ionization is studied within the independent particle approximation and the third-order perturbation theory. Particular attention is paid to how the polarization of the biharmonic light field affects the total rate. The ratios of the biharmonic ionization rates for linearly and circularly polarized beams as well as for corotating and counter-rotating elliptically polarized beams are analyzed, and how they depend on the beam parameters, such as photon frequency or phase between $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ light beams. We show that the interference of the biharmonic ionization amplitudes determines the dominance of a particular beam polarization over another and that it can be controlled by an appropriate choice of beam parameters. Furthermore, we demonstrate our findings for the ionization of neon $L$ shell electrons.

Nonlinear nonreciprocal photocurrents under phonon dressing

Nonlinear optical (NLO) effects have attracted great interest recently. However, most of the computational studies on NLO use the independent particle approximation and ignore many-body effects. Here we develop a generic Green's function framework to calculate the NLO response functions, which can incorporate various many-body interactions. We focus on the electron-phonon coupling and reveal that phonon dressing can make significant impacts on nonlinear photocurrent, such as the bulk photovoltaic (BPV) and bulk spin photovoltaic (BSPV) currents. BPV and BSPV should be zero for centrosymmetric crystals, but when phonons are driven out of equilibrium by, for example, a temperature gradient $\ensuremath{\nabla}T$, the optical selection rules are altered and phonon-pumped BPV and BSPV currents can be nonzero in nominally centrosymmetric crystal. Moreover, we show that such NLO responses under nonequilibrium phonon dressing can be nonreciprocal, as the direction of the current does not necessarily get reversed when the direction of the temperature gradient is reversed.