Framework Of Bethe-Salpeter Equation Research Articles

Optical properties of rutile TiO[formula omitted] with Zr, Mo, Zn, Cd impurities

To explore quasiparticle (QP) energy gaps and photoabsorption spectra of rutile TiO2 with nonmagnetic transition metal (Zr, Mo, Zn, Cd) impurities, we conducted a Γ-point only GW ＋ Bethe–Salpeter equation (BSE) calculation on a 72 (or 71) atom supercell. Our findings reveal that Zn and Cd impurities must coexist, at least partly, with oxygen vacancies to maintain charge neutrality. Among the systems considered, Mo, Zn, or Cd doped rutile TiO2 may exhibit optical absorption and catalytic activity under visible light. The resulting QP energy gaps (ΔɛQP) and photoabsorption energies (PAEs) are fairly in good agreement with both experimental and theoretical data currently available. The necessary conditions for the applicability of the Γ-point only approach in the GW ＋ BSE framework were found to be: (1) The Γ-point only GW calculation should reproduce a reasonable band gap. (2) The “superficial” exciton binding energy (the diagonal element of Wvc;vc−2Xvc;vc between v= VBM and c= CBM, where W and X are the direct and exchange terms of the BSE matrix elements, respectively) must be positive or marginally negative. (3) The “real” exciton binding energy (ΔɛQP− the lowest PAE) should be positive, even if it is exceptionally small.

Phonon screening and dissociation of excitons at finite temperatures from first principles

The properties of excitons, or correlated electron-hole pairs, are of paramount importance to optoelectronic applications of materials. A central component of exciton physics is the electron-hole interaction, which is commonly treated as screened solely by electrons within a material. However, nuclear motion can screen this Coulomb interaction as well, with several recent studies developing model approaches for approximating the phonon screening of excitonic properties. While these model approaches tend to improve agreement with experiment, they rely on several approximations that restrict their applicability to a wide range of materials, and thus far they have neglected the effect of finite temperatures. Here, we develop a fully first-principles, parameter-free approach to compute the temperature-dependent effects of phonon screening within the ab initio [Formula: see text]-Bethe-Salpeter equation framework. We recover previously proposed models of phonon screening as well-defined limits of our general framework, and discuss their validity by comparing them against our first-principles results. We develop an efficient computational workflow and apply it to a diverse set of semiconductors, specifically AlN, CdS, GaN, MgO, and [Formula: see text]. We demonstrate under different physical scenarios how excitons may be screened by multiple polar optical or acoustic phonons, how their binding energies can exhibit strong temperature dependence, and the ultrafast timescales on which they dissociate into free electron-hole pairs.

(γ, χcJ(J = 0,1)) and (γ, ηc) production in electron-positron annihilation at [formula omitted] GeV and 4.6 GeV in the framework of Bethe-Salpeter equation

In present work we study the production of ground and excited charmonium states in e−e+→γχcJ(nP)(J=0,1), and e−e+→γηc(nS), through leading order (LO) diagrams, which proceed through exchange of a virtual photon that couples to γ and ηc/χcJ through the triangular quark loop diagram, in the framework of 4×4 Bethe-Salpeter equation (BSE), at center of mass energies s=10.6 GeV (Belle energy), and 4.6 GeV (BESIII energy). The amplitude simplifies to a general form required by Lorentz-covariance, in terms of its form factors. The cross sections for these processes with leading order diagrams alone at s=10.6 GeV provide a sizable contribution, which might be mainly due to the BSE being a fully relativistic approach that incorporates the relativistic effect of quark spins and can also describe internal motion of constituent quarks within the hadron in a relativistically covariant manner. Our results are compared with recent Belle data at 10.6 GeV, and BESIII data at 4.6 GeV, as well as other models. Plots of cross sections versus the center-of mass energy, s reveal mild fluctuations in their behaviour for all the three processes in the low energy (s=4–6 GeV) region, and are analyzed in terms of the form factors.

WanTiBEXOS: A Wannier based Tight Binding code for electronic band structure, excitonic and optoelectronic properties of solids

The Bethe–Salpeter equation (BSE) approach becomes a methodology commonly used for simulating excitonic and optical properties in computer materials sciences. However, BSE approach based directly on first principles demands a high computational cost, being prohibitive for larger systems. In order to overcome this challenge, we have developed WanTiBEXOS, a parallel computational FORTRAN code, constituted of a maximally localized Wannier functions based tight-binding (MLWF-TB) model in conjunction with BSE framework. The MLWF-TB Hamiltonian used in WanTiBEXOS package can be obtained via any density functional theory package interfaced with Wannier90 code. It's expected, due MLWF-TB formalism, a computational time reduction around one or more orders of magnitude in comparison with BSE ab initio implementations. In order to demonstrate its reliability, flexibility, efficiency and versatility of WanTiBEXOS, we simulate electronic and optical property calculations for the representative materials, including conventional bulk semiconductors, perovskites, nano-monolayer materials and van der Waals heterostructures. Program summaryProgram Title: WanTiBEXOSCPC Library link to program files:https://doi.org/10.17632/4vh76mnkv5.1Developer's repository link:https://github.com/ac-dias/wantibexosLicensing provisions: GNU General Public Licence 3.0Programming language: Fortran90 (Intel compiler)External routines: OpenMP and Intel Math Kernel Library (MKL)Nature of problem: Calculate electronic, optical, and excitonic properties of solids.Solution method: Tight-binding approach under maximally localized Wannier functions (MLWF) parametrization to describe standard electronic properties and the Bethe–Salpeter formalism for excitonic properties.

Mass Spectra and Decay Constants of Heavy-Light Axial Quarkonia in the Framework of Bethe-Salpeter Equation

In this work we calculate the mass spectrum and decay constants of ground and excited states of heavy-light P-wave mesons such as 1++ and 1+−, with quark composition, \(c\overline {u}, c\overline {s}, b\overline {u}, b\overline {s}\), and \(b\overline {c}\) in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure \((\gamma _{\mu }\bigotimes \gamma _{\mu })\) in the interaction kernel, In this 4 × 4 BSE framework, the coupled Salpeter equations for \(Q\overline {q}\) are first solved for the confining part of interaction, and are shown to decouple under heavy-quark approximation. Then the one-gluon-exchange interaction is perturbatively incorporated, leading to their mass spectral equations. The analytic forms of wave functions obtained from these equations are then used for calculation of leptonic decay constants of ground and excited states of 1++, and 1+− as a test of these wave functions and the over all framework.

Perturbative method to estimate meson masses in the framework of the Bethe-Salpeter equation beyond its dominant interaction

We propose a novel method to calculate the meson mass in the framework of Dyson-Schwinger equation and Bethe-Salpeter equation, once their dominant interactions are identified. The method is based on the perturbation theory of matrix, which is widely used in quantum mechanics. Taking interactions other than the dominant ones as perturbations, we derive the first order correction of quark propagator. Implementing the perturbation on BSE, the mass correction at first order is then given. We exemplify this method with the well known Rainbow-Ladder (RL) truncation, and go beyond the RL using a simple model, i.e., the Munczek-Nemirovsky~(MN) model, by studying the pion and $\rho$ mesons mass shift. The results are all in good agreement with those obtained by fully solving the BSE beyond RL. Our perturbative method therefore can be used to give a semi-quantitative estimate of meson mass correction in cases when the BSEs are complicated by interactions that go beyond the dominant one.

Analytic approach to calculations of mass spectra and decay constants of heavy-light quarkonia in the framework of Bethe-Salpeter equation

This work is an extension of the work in [Phys. Rev. D 97, 034021 (2018)] to ground and excited states of ${0}^{++}$, ${0}^{\ensuremath{-}+}$, and ${1}^{\ensuremath{-}\ensuremath{-}}$ of heavy-light ($c\overline{u},c\overline{s},b\overline{u},b\overline{s}$, and $b\overline{c}$) quarkonia in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure (${\ensuremath{\gamma}}_{\ensuremath{\mu}}\ensuremath{\bigotimes}{\ensuremath{\gamma}}_{\ensuremath{\mu}}$) in the interaction kernel, in contrast to the approximate treatment of the same in our previous works [H. Negash and S. Bhatnagar, Int. J. Mod. Phys. E 25, 1650059 (2016)., S. Bhatnagar and L. Alemu, Phys. Rev. D 97, 034021 (2018).]). In this $4\ifmmode\times\else\texttimes\fi{}4$ BSE framework, the coupled Salpeter equations for $Q\overline{q}$ (that are more involved than the equal mass ($Q\overline{Q}$) mesons) are first shown to decouple for the confining part of interaction, under heavy-quark approximation, and analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to their mass spectral equations. The analytic forms of wave functions obtained from these equations are then used for calculation of leptonic decay constants of ground and excited states of ${0}^{\ensuremath{-}+}$ and ${1}^{\ensuremath{-}\ensuremath{-}}$ as a test of these wave functions and the over all framework.

Approach to calculation of mass spectra and two-photon decays of cc¯ mesons in the framework of Bethe-Salpeter equation

In this work we calculate the mass spectra of charmonium for $1P,\dots{},4P$ states of ${0}^{++}$ and ${1}^{++}$, for $1S,\dots{},5S$ states of ${0}^{\ensuremath{-}+}$, and for $1S,\dots{},4D$ states of ${1}^{\ensuremath{-}\ensuremath{-}}$ along with the two-photon decay widths of the ground and first excited states of ${0}^{++}$ quarkonia for the process ${O}^{++}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this $4\ifmmode\times\else\texttimes\fi{}4$ BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of ${\ensuremath{\chi}}_{c0}$. Our results are in reasonable agreement with data (where available) and other models.

Radiative Decay Widths of Ground and Excited States of Vector Charmonium and Bottomonium

We study the radiative decay widths of vector quarkonia for the process of J/ψ(nS)→ηc(nS)γ and Υ(nS)→ηb(nS)γ (for principal quantum numbers n=1,2,3) in the framework of Bethe-Salpeter equation under the covariant instantaneous ansatz using a 4×4 form of BSE. The parameters of the framework were determined by a fit to the mass spectrum of ground states of pseudoscalar and vector quarkonia, such as ηc, ηb, J/ψ, and Υ. These input parameters so fixed were found to give good agreements with data on mass spectra of ground and excited states of pseudoscalar and vector quarkonia, leptonic decay constants of pseudoscalar and vector quarkonia, two-photon decays, and two-gluon decays of pseudoscalar quarkonia in our recent paper. With these input parameters so fixed, the radiative decay widths of ground (1S) and excited (2S,3S) states of heavy vector quarkonia (J/Ψ and Υ) are calculated and found to be in reasonable agreement with data.

Mass spectrum and leptonic decay constants of ground and radially excited states of ηc and ηb in a Bethe–Salpeter equation framework

In this paper, we study the mass spectrum and decay constants of ground state (1S) and radially excited states (2S and 3S) of heavy equal mass pseudoscalar mesons, ηc and ηb. We have employed the framework of Bethe–Salpeter equation (BSE) under Covariant Instantaneous Ansatz (CIA). Our predictions are in reasonable agreement with the data on available states and results of other models.

Electronic and optical properties of cadmium fluoride: The role of many-body effects

Electronic excitations and optical spectra of CdF${}_{2}$ are calculated up to ultraviolet employing state-of-the-art techniques based on density functional theory and many-body perturbation theory. The GW scheme proposed by Hedin has been used for the electronic self-energy to calculate single-particle excitation properties as energy bands and densities of states. For optical properties many-body effects, treated within the Bethe-Salpeter equation framework, turn out to be crucial. A bound exciton located about 1 eV below the quasiparticle gap is predicted. Within the present scheme the optical absorption spectra and other optical functions show an excellent agreement with experimental data. Moreover, we tested different schemes to obtain the best agreement with experimental data. Among the several schemes, we suggest a self-consistent quasiparticle energy scheme.

Implementation and testing of Lanczos-based algorithms for Random-Phase Approximation eigenproblems

The treatment of the Random-Phase Approximation Hamiltonians, encountered in different frameworks, like time-dependent density functional theory or Bethe–Salpeter equation, is complicated by their non-Hermicity. Compared to their Hermitian Hamiltonian counterparts, computational methods for the treatment of non-Hermitian Hamiltonians are often less efficient and less stable, sometimes leading to the breakdown of the method. Recently [Grüning et al. Nano Lett. 8 (2009) 2820], we have identified that such Hamiltonians are usually pseudo-Hermitian. Exploiting this property, we have implemented an algorithm of the Lanczos type for Random-Phase Approximation Hamiltonians that benefits from the same stability and computational load as its Hermitian counterpart, and applied it to the study of the optical response of carbon nanotubes. We present here the related theoretical grounds and technical details, and study the performance of the algorithm for the calculation of the optical absorption of a molecule within the Bethe-Salpeter equation framework.

Spectrum for heavy quarkonia and mixture of the relevant wave functions within the framework of Bethe-Salpeter equation

Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) still missing in experimental observations and potential applications of the relevant wave functions of the bound states, we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to potential of non-relativistic quark model, is instantaneous, so we call the corresponding B.S. equation as BS-In equation throughout the paper. Particularly, a new way to solve the B.S. equation, which is different from the traditional ones, is proposed here, and with it not only the known spectrum for the heavy quarkonia is re-generated, but also an important issue is brought in, i.e., the obtained solutions of the equation `automatically' include the 'fine', 'hyperfine' splittings and the wave function mixture, such as $S-D$ wave mixing in $J^{PC}=1^{--}$ states, $P-F$ wave mixing in $J^{PC}=2^{++}$ states for charmonium and bottomonium etc. It is pointed out that the best place to test the wave mixture probably is at $Z$-factory ($e^+e^-$ collider running at $Z$-boson pole with extremely high luminosity).

Relativistic three-particle problem and heavy quarks

Strong binding of three scalar quarks is investigated in the framework of Bethe-Salpeter equations. After stating the relevant field-theoretic formulae, possible dynamical assumptions are discussed which can help to describe the observed baryon mass spectrum. Just as in the quark-antiquark case a covariant harmonic oscillator approximation may be formulated, and it is shown that this corresponds to linear Regge trajectories. The resulting Bethe-Salpeter amplitude of the ground state is used in a calculation of the electromagnetic radius by means of the triangle graph model. The oscillator constant as obtained by matching the Regge slope leads, independently of the quark mass, to 0.8 fm for the e.m. radius.