Salpeter Equation Research Articles

λ and ρ Regge trajectories for hidden bottom and charm tetraquarks (Qq)(Q¯q¯′)

We propose the Regge trajectory relations for the heavy tetraquarks (Qq)(Q¯q¯′) (Q=b,c;q,q′=u,d,s) with hidden bottom and charm. By employing the new relations, both the λ-trajectories and the ρ-trajectories for the tetraquarks (Qq)(Q¯q¯′) can be discussed. The masses of the λ-mode excited states and the ρ-mode excited states are estimated, and they agree with other theoretical predictions. We show that the behaviors of the ρ-trajectories are different from those of the λ-trajectories. The ρ-trajectories behave as M∼xρ1/2 (xρ=nr,l) while the λ-trajectories behave as M∼xλ2/3 (xλ=Nr,L). Moreover, the Regge trajectory behaviors for other types of tetraquarks are investigated based on the spinless Salpeter equation. We show that both the λ-trajectories and the ρ-trajectories are concave downward in the (M2,x) plane. The Regge trajectories for the tetraquarks containing the light diquark and/or the light antidiquark also are concave in the (M2,x) plane when the masses of the light constituents are included and the confining potential is linear. Published by the American Physical Society 2024

Tuning the optical absorption and exciton bound states of germanene by chemical functionalization

We present a comprehensive study of buckled honeycomb germanene functionalized with alternately bonded side groups hydroxyl (–H), methyl (–CH3) and trifluoro methyl (–CF3). By means of most modern theoretical and computational methods we determine the atomic geometries versus the functionalizing groups. The quasiparticle excitation effects on the electronic structure are taken into account by means of exchange-correlation treatment within the GW framework. The Bethe–Salpeter equation is solved ab initio to derive optical spectra including excitonic and quasiparticle effects. Band edge excitons are investigated in detail. The binding properties are compared with those resulting from model studies. The functionalization leads to significantly modified band structures compared with pristine germanene. The Dirac bands near the K point are destroyed and direct gaps appear at the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma$$\\end{document} point. Together with the many-body effects, quasiparticle gaps of 2.3, 1.8 or 1.0 eV result for –H, –CH3 and –CF3 functionalization. Totally different absorption spectra are found for in-plane and out-of-plane light polarization. Strongly bound excitons are visible below the quasiparticle band edge with binding energies of about 0.5, 0.4 or 0.3 eV. The nature of these band-gap excitons is investigated via their wave function, the contribution of various interband combinations and the dipole selection rules.

One-dimensional magnetic excitonic insulators

Abstract Dimensionality significantly affects exciton production and condensation. Despite the report of excitonic instability in one-dimensional materials, it remains unclear whether these spontaneously produced excitons can form Bose–Einstein condensates. In this work, we first prove statistically that one-dimensional condensation exists when the spontaneously generated excitons are thought of as an ideal neutral Bose gas, which is quite different from the inability of free bosons to condense. We then derive a general expression for the critical temperature in different dimensions and find that the critical temperature increases with decreasing dimension. We finally predict by first-principles GW-Bethe–Salpeter equation calculations that experimentally accessible single-chain staircase Scandocene and Chromocene wires are an antiferromagnetic spin-triplet excitonic insulator and a ferromagnetic half-excitonic insulator, respectively.

Stochastic Schrödinger equation for hot-carrier dynamics in plasmonic systems

We present a multiscale method coupling the theory of open quantum systems with real-time ab initio treatment of electronic structure to study hot-carrier dynamics in photoexcited plasmonic systems. We combine the Markovian Stochastic Schrödinger equation with an ab initio GW coupled to the Bethe–Salpeter (BSE) equation description of the electronic degrees of freedom, interacting with a metallic nanoparticle modeled classically according to the polarizable continuum model. We apply this methodology to study the effect of relaxation (T1) and pure dephasing (T2) times on the hot-carrier dynamics in a system composed of a quantum portion described at GW/BSE level, i.e., a CHO fragment adsorbed on a vertex of a rhodium nanocube, and of the rest of the nanocube, treated classically, when irradiated with a 2.7 eV light pulse, inspired by the experimental results on plasmon-driven CO2 photoreduction. A net hole injection from rhodium to CHO is observed, with and without the classical portion of the nanocube. The nanocube effect is to enhance the generated charge population by two orders of magnitude. The nonradiative decay, via a relaxation time T1 based on the energy-gap law, produces a rapid decrease of the charge population. Results with T2 only show that a charge injection retarded with respect to the pulse, which is present in the coherent dynamics, disappears when coherence is erased.

Excitonic properties and solar harvesting performance of Cs2ZnY2X2 as quasi-2D mixed-halide perovskites

Due to their low toxicity and high-temperature stability, lead-free quasi-2D metal halide perovskites (MHPs) are promising materials for optoelectronic applications. However, understanding their structural and optoelectronic properties, especially excitonic effects (electron-hole pair, e-h), is challenging due to their quantum well topology. We propose an efficient protocol for band gap correction of Cs2ZnX (X = Cl4, Br2Cl2, and I2Cl2) and Cs2PbI2Cl2 (used as a benchmark) quasi-2D MHPs. This protocol is based on a relativistic quasiparticle approach (DFT-1/2) using density functional theory (DFT). We first examined the hybrid contributions of the halide alloys, leading to excitonic characterization using the Bethe–Salpeter equation within the maximally localized Wannier functions tight-binding method. This method provides a cost-effective approach for describing e-h quasiparticle effects. Additionally, we analyzed the crystal structure, thermodynamic stability, and optoelectronic properties of the newly synthesized Zn-based systems, focusing on their structural stability mechanisms. We found a correlation between the allocation of Cs+ cations in the crystal structure and the formation of two distinct stabilization patterns, influenced by the radii of the metal (Zn or Pb) and halide components. The relativistic correction of the band gap energies yielded results within 10 % of the experimental values. Furthermore, incorporating e-h quasiparticle effects for Cs2PbI2Cl2 resulted in an exciton binding energy of 0.160 eV, in excellent agreement with experimental data. This work represents a significant advance in the optoelectronic characterization of Cs2ZnX systems, previously unexplored for their excitonic properties.

Strain tunable excitonic optical properties in monolayer Ga2O3

Abstract Two-dimensional (2D) Ga2O3 has been confirmed to be a stable structure with five atomic layer thickness configuration. In this work, we study the quasi-particle electronic band structures and then access the excitonic optical properties through solving the Bethe–Salpeter equation (BSE). The results reveal that the exciton dominates the optical absorption in the visible light region with the binding energy as large as ∼ 1.0 eV, which is highly stable at room temperature. Importantly, both the dominant absorption P1 and P2 peaks are optically bright without dark exciton between them, and thus is favorable for luminescence process. The calculated radiative lifetime of the lowest-energy exciton is 2.0×10−11 s at 0 K. Furthermore, the radiative lifetime under +4% tensile strain is one order of magnitude shorter than that of the strain-free case, while it is less insensitive under the compressive strain. Our findings set the stage for future theoretical and experimental investigation on monolayer Ga2O3.

Discovery of novel silicon allotropes with optimized band gaps to enhance solar cell efficiency through evolutionary algorithms and machine learning

In the pursuit of advancing solar energy technologies, this study presents 20 direct and quasi-direct band gap silicon crystalline semiconductors that satisfy the Shockley-Queisser limit, a benchmark for solar cell efficiency. Employing two evolutionary algorithm-based searches, we optimize structures and calculate fitness function using the DFTB method and Gaussian approximation potential. Following the preselection of structures based on energy considerations, we further optimize them using PBEsol DFT. Subsequently, we screen the structures based on their band gap, employing a DFTB method tailored for band gap calculation of silicon crystals. To ensure accurate band gap determination, we employ HSE and GW methods. To validate the structural stability, we employ phonon analysis via linear regression algorithm applied to PBEsol DFT data. Significantly, the structures unveiled in this study are of great importance due to their proven stability from both mechanical and dynamic perspectives. Furthermore, the ductility and low density of certain structures enhance their potential application. We examine the optical properties by studying the imaginary part of the dielectric function by solving the Bethe–Salpeter Equation on top of GW approximation. By calculating the SLME, we achieve an efficiency of 32.7% for Si22 at a thickness of 500 nm. Moreover, the study harnesses various machine learning algorithms to develop a predictive model for the band gap energy of these silicon structures. Input data for machine learning models are derived from structural MBTR and SOAP descriptors, as well as DFT outputs. Notably, the results reveal that features extracted from DFT outperform the MBTR and SOAP descriptors.

Excitonic optical properties in monolayer SnP2S6

Abstract Quantum confinement effect and reduced dielectric screening in two-dimensional (2D) dramatically enhance the electron–hole interactions. In this work, we use many-body perturbation theory and Bethe–Salpeter equation (BSE) to investigate the electronic and excitonic optical properties of monolayer SnP2S6. Our findings reveal that the excitonic effect dominates the optical absorption spectra in the visible light range, and the lowest-energy exciton X 0 in monolayer SnP2S6 is optically bright with the binding energy of 0.87 eV and the radiative lifetime of ∼ 10−11 s, which is highly advantageous to the photo-luminescence. Most importantly, the absence of optically forbidden states below the bright states X 0 would give rise to a high quantum efficiency of 2D SnP2S6. We also find that applied biaxial strain can further shorten the radiative lifetime of the bright states. These results imply that 2D SnP2S6 is a promising candidate for the optoelectronic devices.

Excitonic and optoelectronic investigations of bromide-chloride mixed vacancy-ordered double tellurium perovskite systems

Metal-halide perovskites, including vacancy-ordered double perovskites, are versatile semiconductors with applications in photovoltaics and sensors. Here we explore the structural stability, electronic and optical properties of Cs2Te(Br1-xClx)6 series using first-principles-based on density functional theory and state-of-the-art many-body perturbation theory. Our study reveals consistent energy levels across different crystal structures obtained by varying Cl concentrations, indicating uniform structural stability. By employing hybrid density functional theory with spin-orbit coupling, we analyze the effect of Cl-site substitutions on electronic and optical properties. We observe a quasi-linear relationship between band gap and Cl concentration in Cs2Te(Br1-xClx)6 compositions, with alloying resulting in a redshift in the optical absorption coefficient. Moreover, we explore electron-hole interactions using the GW approximation and Bethe−Salpeter equation, revealing exciton binding energies and dark-bright splitting. Remarkably, exciton binding energies, reaching up to 930 meV, can be finely tuned through substitutional engineering. Finally, we investigate the thermoelectric properties of the Br/Cl mixed halide double perovskites, suggesting promising prospects for their application as thermoelectric materials.

Excited‐State Dynamics and Optical Properties of Silica Under Ultrafast Laser Irradiation

AbstractExcited by intense infrared ultrafast light pulses, a wide bandgap material undergoes nonlinear ionization, generating a high density of free electrons in conduction states. As a result, the electronic band structure is critically modified and the bandgap shrinks. This induces rapid changes in optical properties, dramatically affecting the absorption spectrum during light coupling to the dielectric surface or during nonlinear propagation inside the bulk. This study analyzes the structural behavior and the modification of the optical properties of laser‐excited silica glass at the molecular cluster level through first‐principles simulations. Employing density functional theory and the GW approximations for band structure under nonequilibrium conditions, alongside the Bethe–Salpeter equation, the dynamics of the optical properties of fused silica are comprehensively explored. The behavior of excited fused silica in a wide photon energy range (from a few to 20 eV) is thus predicted. Laser‐induced electron excitation triggers a redistribution of charges between oxygen and silicon atoms, accompanied by a significant increase in electronic pressure, local atomic structure rearrangement, and material expansion. Molecular dynamics simulations offer a temporal perspective on the excited state dynamics, unveiling the intricate interplay between electronic and atomic effects on bandgap evolution. The analysis sheds light on excitonic resonances, intraband and interband transitions in fused silica under ultrafast laser irradiation, providing valuable insights into its excited state behavior and optical properties.

Strain-induced changes of electronic and optical properties of Zr-based MXenes

Zr-based MXenes recently attracted attention because of its experimental preparation showing temperature stability, mechanical strength, and promising energy, sensoric, and electrochemistry applications. However, necessary theoretical predictions at a precise/predictive level are complicated due to essential excitonic features and strong electron correlation (i.e., a necessity to go beyond standard density functional theory, DFT). Contrary to the prevailing focus on oxygen-terminated MXenes and standard predictions of other Zr-based MXenes as conductors, based on the hybrid DFT and GW many-body perturbational theory, we were able to find seven different semiconductors (five of them for their equilibrium geometry and two others under slight tensile biaxial strain) in the case of two- and three-layered Zr2CT2 and Zr3C2T2 configurations with various terminations (T = O, F, S, Cl). We observed semiconductor-to-conductor transition induced by strain in the majority of such Zr-based MXenes at an experimentally achievable strain range. Furthermore, using the Bethe–Salpeter equation (BSE), we demonstrated that selected semiconducting Zr-based MXenes possess high optical absorption efficiency (20%–30%) in the visible light range, underscoring their potential in photonic applications. The high sensitivity of Zr-based MXenes to external conditions and functionalization combined with the thermal stability makes the materials promising for applications at operational temperatures in electronic and optical technologies.

Classical and quantum theory of fluctuations for many‐particle systems out of equilibrium

AbstractCorrelated classical and quantum many‐particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging both, conceptionally and with respect to computational resources. While for classical systems, in principle, exact simulations are possible via molecular dynamics, this is not the case for quantum systems. Alternatively, one can use many‐particle approaches such as hydrodynamics, kinetic theory, or nonequilibrium Green functions (NEGF). However, NEGF exhibit a very unfavorable cubic scaling of the CPU time with the number of time steps. An alternative is the G1–G2 scheme [N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)] which allows for NEGF simulations with time linear scaling, however, at the cost of large memory consumption. The reason is the need to store the two‐particle correlation function. This problem can be overcome for a number of approximations by reformulating the kinetic equations in terms of fluctuations – an approach that was developed, for classical systems, by Yu.L. Klimontovich [JETP 33, 982 (1957)]. Here, we present an overview of his ideas and extend them to quantum systems. In particular, we demonstrate that this quantum fluctuations approach can reproduce the nonequilibrium GW approximation [E. Schroedter et al., Cond. Matt. Phys. 25, 23401 (2022)] promising high accuracy at low computational cost which arises from an effective semiclassical stochastic sampling procedure. We also demonstrate how to extend the approach to the two‐time exchange‐correlation functions and the density response properties. [E. Schroedter et al., Phys. Rev. B 108, 205109 (2023)]. The results are equivalent to the Bethe–Salpeter equation for the two‐time exchange‐correlation function when the generalized Kadanoff‐Baym ansatz with Hartree‐Fock propagators is applied [E. Schroedter and M. Bonitz, phys. stat. sol. (b) 2024, 2300564].

Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory.

Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's function approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, the quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.

Signature of excitonic insulators in phosphorene nanoribbons

Phosphorene is a recently developed two-dimensional (2D) material that has attracted tremendous attention because of its unique anisotropic optical properties and quasi-one-dimensional (1D) excitons. We use first-principles calculations combined with the maximally localized Wannier function tight binding Hamiltonian and Bethe–Salpeter equation (BSE) formalism to investigate quasiparticle effects of 2D and quasi-1D blue and black phosphorene nanoribbons. Our electronic structure calculations shows that both blue and black monolayered phases are semiconductors. On the other hand black phosphorene zigzag nanoribbons are metallic. Similar behavior is found for very thin blue phosphorene zig-zag and armchair nanoribbon. As a general behavior, the exciton binding energy decreases as the ribbon width increases, which highlights the importance of quantum confinement effects. The solution of the BSE shows that the blue phosphorene monolayer has an exciton binding energy four times higher than that of the black phosphorene counterpart. Furthermore, both monolayers show a different linear optical response with respect to light polarization, as black phosphorene is highly anisotropic. We find a similar, but less pronounced, optical anisotropy for blue phosphorene monolayer, caused exclusively by the quasi-particle effects. Finally, we show that some of the investigated nanoribbons show a spin-triplet excitonic insulator behavior, thus revealing exciting features of these nanoribbons and therefore provides important advances in the understanding of quasi-one dimensional phosphorus-based materials.

Computation of the expectation value of the spin operator S^2 for the spin-flip Bethe–Salpeter equation

Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator S^2 . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of ⟨S^2⟩ may be found to differ from 2.00; this difference is called ‘spin contamination’. The expectation values ⟨S^2⟩ must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for ⟨S^2⟩ as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating ⟨S^2⟩ , we present the derivation for the general equation for computing ⟨S^2⟩ with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.

Multi-objective global optimization approach predicted quasi-layered ternary TiOS crystals with promising photocatalytic properties

Abstract Titanium dioxide (TiO2) has attracted considerable research attentions for its promising applications in solar cells and photocatalytic devices. However, the intrinsic challenge lies in the relatively low energy conversion efficiency of TiO2, primarily attributed to the substantial band gaps (exceeding 3.0 eV) associated with its rutile and anatase phases. Leveraging multi-objective global optimization, we have identified two quasi-layered ternary Ti–O–S crystals, composed of titanium, oxygen, and sulfur. The calculations of formation energy, phonon dispersions, and thermal stability confirm the chemical, dynamical and thermal stability of these newly discovered phases. Employing the state-of-art hybrid density functional approach and many-body perturbation theory (quasiparticle GW approach and Bethe–Salpeter equation), we calculate the optical properties of both the TiOS phases. Significantly, both phases show favorable photocatalytic characteristics, featuring band gaps suitable for visible optical absorption and appropriate band alignments with water for effective charge carrier separation. Therefore, ternary compound TiOS holds the potential for achieving high-efficiency photochemical conversion, showing our multi-objective global optimization provides a new approach for novel environmental and energy materials design with multicomponent compounds.

Abnormal Solutions of Bethe–Salpeter Equation with Massless and Massive Exchanges

Abnormal Solutions of Bethe–Salpeter Equation with Massless and Massive Exchanges

Production of Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document} in B nonleptonic decays

In 2021, a new charm-strange meson, Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document}, was discovered, which is believed to be the Ds+(21S0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_s^+(2^1S_0)$$\\end{document}. However, its low mass and wide width are challenged by theoretical results. Given the small branching ratio of the current production channel, resulting in a small number of events and large errors, we suggest searching for the Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document} in the B meson nonleptonic decays, Bq→Dq(∗)Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_q\\rightarrow D^{(*)}_qD_{s0}(2590)^+$$\\end{document} (q=u,d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q=u,d$$\\end{document}), followed by Ds0(2590)+→D∗K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+\\rightarrow D^*K$$\\end{document}. We find that Br(Bq→Dq(∗)Ds0(2590)+)×Br(Ds0(2590)+→D∗K)=(2.16∼2.82)×10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Br(B_q\\rightarrow D^{(*)}_qD_{s0}(2590)^+)\ imes Br(D_{s0}(2590)^+\\rightarrow D^{*}K)=(2.16\\sim 2.82)\ imes 10^{-3}$$\\end{document} is very large, and the result is not sensitive to the mass of Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document}. Due to the large branching ratio, numerous Ds0(2590)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{s0}(2590)^+$$\\end{document} events are expected. This study is based on the framework of the instantaneous Bethe–Salpeter equation, and the relativistic wave functions used for mesons contain different partial waves. The contributions of the different partial waves are also studied.

Tailoring the optoelectronic properties of MoS2 for broadband photodetection: Showcasing an Ab-into study involving the quasi-particle correction within the Green’s function-based approximation

In this study, the electronic and structural characteristics of both bulk and monolayer hexagonal MoS2 material are studied within and beyond density functional theory (DFT) by considering one-shot GW corrections for an accurate band gap prediction. Interestingly, our computed quasiparticle (QP) bandgap of 1.36 eV and 3.33 eV for bulk and monolayer, respectively, is in excellent agreement with the experimental finding. The elucidation of the optical properties was estimated with the aid of the Bethe–Salpeter equation within the many-body perturbation theory (MPB). The computed optical transitions such as absorption coefficient, extinction coefficient, refractive index, reflectivity, and electron energy loss function are in better agreement with the experimental data. Moreover, the new approach allows for the efficient inclusion of all conduction bands in GW calculations, significantly reducing computational costs compared to traditional methods. A good agreement of the lattice parameters, as well as the interlayer distance with the experimental findings, is observed by the inclusion of van der Waals (vdW) corrections. Besides the agreement with previously reported values, the evaluated band structure determined with the quasiparticle corrections shows that both bulk and monolayer MoS2 material exhibit semiconducting properties with direct and indirect band gaps, respectively. The calculation of the density of states reveals that the s-orbitals of S atoms and the d-orbitals of Mo are predominantly at the origin of the essential material properties secured at the Fermi level. The results of the study also point to the possibility of a foundation for creating physical structures with swift, decisive, directed, and long-range broadband photodetection capabilities.

Multiple scattering, radiative transfer, and parameter regimes

We have established the radiative transfer regime in a four-parameter space spanned by amplitude and scale of fluctuations, convergence rate, and spatial range. The derivation of radiative transfer equations from wave equations offers a better understanding of the underlying physics in radiative transfer theory. One approach is based on tools borrowed from quantum field theory (QFT) and employs the Dyson and Bethe–Salpeter equations as the foundation. This has allowed us to investigate the small scale fluctuation regime, kl = O ( ε ) . We also investigated this regime using the scale-separated asymptotics approach and found that the conditions on the parameters are the same as in the QFT approach if the convergence rate of the Dyson series is O ( ε 2 ) . Furthermore, we found that there is a multitude of regimes where radiative transfer manifests. We hence infer that for a fixed spatial range, increase in the scale size of fluctuations leads to decrease in the upper bound of variance of permittivity fluctuations along with diminished convergence rate of the Wigner series. Also, for a fixed scale size and convergence rate, the spatial range where radiative transport manifests decreases with increase in strength of fluctuations.