Hartree Potential Research Articles

Reactive scattering of H2 on Cu(111) at 925K: Effective Hartree potential vs sudden approximation.

We present new quantum dynamical results for the reactive scattering of hydrogen molecules from a Cu(111) surface at a surface temperature of 925K. Reaction, scattering, and diffraction probabilities are compared for results obtained using both an effective Hartree potential (EfHP) and a sudden approximation approach, implemented through the static corrugation model (SCM), to include surface temperature effects. Toward this goal, we show how the SRP48 DFT-functional and an embedded atom potential perform when used to calculate copper lattice constants and thermal expansion coefficients based on lattice dynamics calculations within the quasi-harmonic approximation. The so-calculated phonons are then used in the EfHP approach to replace the normal modes of a fictitious copper cluster used in earlier work. We find that both the EfHP and SCM approaches correctly predict the reaction probability curve broadening effect when the surface temperature is increased. Similarly, results for rovibrationally elastic scattering appear to be improved, predominantly for the SCM model. The behavior of the EfHP results appears to remain much closer to that of a Born-Oppenheimer static surface approach, which excludes any surface temperature effects. Finally, for the diffraction, we show very clear attenuation effects for the SCM approach, significantly decreasing specular diffraction probabilities at 925K surface temperature. These results demonstrate that state-of-the-art theoretical models are able to reproduce strictly quantum mechanical scattering effects with a sudden approximation model and open up interesting opportunities for further comparisons to experimental diffraction results.

Towards chemical accuracy using a multi-mesh adaptive finite element method in all-electron density functional theory

Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn–Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn–Sham wavefunctions but also the Hartree potential, should be approximated accurately. Under the adaptive finite element framework, this can be implemented by constructing the a posteriori error indicator based on approximations of the aforementioned two quantities. However, this way results in a large amount of computational cost. To reduce the computational cost, we propose a novel solver for the Kohn–Sham equation by using the multi-mesh adaptive technique, in which the Kohn–Sham equation and the Poisson equation are solved in two different meshes on the same computational domain, respectively. With the proposed method, chemical accuracy can be achieved with less computational consumption compared with the adaptive method on a single mesh, as demonstrated in a number of numerical experiments.

Density functional theory from spherically symmetric densities: Ground and excited states of Coulomb systems.

Recently, Theophilou [J. Chem. Phys. 149, 074104 (2018)] proposed a peculiar version of the density functional theory by showing that the set of spherical averages of the density around the nuclei determines uniquely the external potential in atoms, molecules, and solids. Here, this novel theory is extended to individual excited states. The generalization is based on the method developed in the series of papers by Ayers, Levy, and Nagy [Phys. Rev. A 85, 042518 (2012)]. Generalized Hohenberg-Kohn theorems are proved to the set of spherically symmetric densities using constrained search. A universal variational functional for the sum of the kinetic and electron-electron repulsion energies is constructed. The functional is appropriate for the ground state and all bound excited states. Euler equations and Kohn-Sham equations for the set are derived. The Euler equations can be rewritten as Schrödinger-like equations for the square root of the radial densities, and the effective potentials in them can be expressed in terms of wave function expectation values. The Hartree plus exchange-correlation potentials can be given by the difference of the interacting and the non-interacting effective potentials.

Efficient all-electron hybrid density functionals for atomistic simulations beyond 10 000 atoms.

Hybrid density functional approximations (DFAs) offer compelling accuracy for abinitio electronic-structure simulations of molecules, nanosystems, and bulk materials, addressing some deficiencies of computationally cheaper, frequently used semilocal DFAs. However, the computational bottleneck of hybrid DFAs is the evaluation of the non-local exact exchange contribution, which is the limiting factor for the application of the method for large-scale simulations. In this work, we present a drastically optimized resolution-of-identity-based real-space implementation of the exact exchange evaluation for both non-periodic and periodic boundary conditions in the all-electron code FHI-aims, targeting high-performance central processing unit (CPU) compute clusters. The introduction of several new refined message passing interface (MPI) parallelization layers and shared memory arrays according to the MPI-3 standard were the key components of the optimization. We demonstrate significant improvements of memory and performance efficiency, scalability, and workload distribution, extending the reach of hybrid DFAs to simulation sizes beyond ten thousand atoms. In addition, we also compare the runtime performance of the PBE, HSE06, and PBE0 functionals. As a necessary byproduct of this work, other code parts in FHI-aims have been optimized as well, e.g., the computation of the Hartree potential and the evaluation of the force and stress components. We benchmark the performance and scaling of the hybrid DFA-based simulations for a broad range of chemical systems, including hybrid organic-inorganic perovskites, organic crystals, and ice crystals with up to 30 576 atoms (101 920 electrons described by 244 608 basis functions).

On the quantum dynamical treatment of surface vibrational modes for reactive scattering of H2 from Cu(111) at 925 K.

We construct the effective Hartree potential for H2 on Cu(111) as introduced in our earlier work [Dutta et al., J. Chem. Phys. 154, 104103 (2021), and Dutta et al., J. Chem. Phys. 157, 194112 (2022)] starting from the same gas-metal interaction potential obtained for 0K. Unlike in that work, we now explicitly account for surface expansion at 925K and investigate different models to describe the surface vibrational modes: (i) a cluster model yielding harmonic normal modes at 0K and (ii) slab models resulting in phonons at 0 and 925K according to the quasi-harmonic approximation-all consistently calculated at the density functional theory level with the same exchange-correlation potential. While performing dynamical calculations for the H2(v = 0, j = 0)-Cu(111) system employing Hartree potential constructed with 925K phonons and surface temperature, (i) the calculated chemisorption probabilities are the highest compared to the other approaches over the energy domain and (ii) the threshold for the reaction probability is the lowest, in close agreement with the experiment. Although the survival probabilities (v' = 0) depict the expected trend (lower in magnitude), the excitation probabilities (v' = 1) display a higher magnitude since the 925K phonons and surface temperature are more effective for the excitation process compared to the phonons/normal modes obtained from the other approaches investigated to describe the surface.

Laser-field-mediated Rashba and Dresselhaus spin–orbit control in GaInAs/AlInAs quantum wells

For more possibilities in exploring the spin–orbit (SO) control in two-dimensional (2D) semiconductor quantum wells, we resort to the laser field by constructing a generic model including both the axial and transverse field components relative to the well-growth direction, with the axial one primarily modifying the structural potential of the well and the transverse one mainly altering the electron density of states and so the Hartree potential. For GaInAs/AlInAs quantum wells with two-subband occupation, we obtain the full scenario of the laser-field response of the Rashba and Dresselhaus SO couplings, including both the intrasubband (αν and βν with ν = 1,2 denoting the subband index) and intersubband (η and Γ) types, by solving the Poisson–Schrödinger equations. Remarkably, for the Dresselhaus coupling, which is insensitive to the electrical manipulation, we demonstrate that it can be substantially tuned by the laser field and unified SO control of different subbands is possible, suggesting that the optical manner is an effective supplement to the electrical means. Moreover, symmetric (α1=−α2) and selective (α1=0, α2≠0) control of the Rashba coupling of different subbands are also observed with the interplay of the two laser components, which are desirable for the realization of skyrmion lattice and the suppression of spin relaxation of given subbands. Besides, for the intersubband coupling, the Rashba term η is optically tunable while the Dresselhaus term Γ is basically immune to the laser field, i.e., selective control of the intersubband coupling by virtue of optical means. These diverse laser-field-mediated SO features offer exciting possibilities in incorporating 2D quantum wells for new applications in the field of spintronics.

DFT based atomic modeling and temperature analysis on the RF and VTC curve of high-k dielectric layer-assisted NCFET

In this report, Density Functional Theory (DFT) based calculation using a Quantum Atomistic Tool Kit (ATK) simulator is done for the hafnia-based ferroelectric material. The band structure, projected density of states (PDOS), and Hartree potential (VH) are taken into account for hafnium oxide (HfO2) and silicon-doped hafnium oxide (Si-doped HfO2). Further, we analyze the temperature variation impact on analog parameters and voltage transfer characteristic (VTC) curve of inverter application of Modified Negative Capacitance Field-Effect-Transistor (NCFET) using the Visual Technology-Computer-Aided-Design (TCAD) simulator. The Modified NCFET structure enhances the DC parameters like leakage current (IOFF) and Subthreshold Swing (SS) compared to the conventional NCFET structure. With the temperature impact, the variation in the parameters of Modified NCFET is discussed at 250 K, 275 K, 300 K, 325 K, and 350 K like transconductance (gm), output conductance (gd), early voltage (VEA) shows the increment as we move from 250 K to 350 K. The short channel effects (SCEs) like Drain Induced Barrier Lowering (DIBL) and Subthreshold Swing (SS) decrease with the temperature fall at 32.98% and 34.74%, respectively. Further, the VTC curve, Noise Margin (NM), and propagation delay of Modified NCFET-based inverter are discussed with the impact of temperature. The propagation delay for the circuit decreased by 67.94% with the rise in the temperature. These factors show that the Modified NCFET-based inverter gives a fast switching performance at high temperatures.

Photoluminescence of GaAsSb/AlAsSb superlattices for investigating band structure

To study the band structure of GaAsSb/AlAsSb systems grown on InP substrates, optical absorption and photoluminescence (PL) measurements were performed. The measurements utilized GaAsSb/AlAsSb superlattice (SL) samples to investigate the optical properties of the system. By comparing optical absorption and photoluminescence (PL) measurements, it was determined that the non-radiative transition occurred at lower energy levels than the PL transition energy in the sample with the narrowest well width. The excitation power dependence of PL measurements exhibited an almost linear power law of peak intensity, suggesting high-quality luminescence properties of GaAsSb/AlAsSb SLs. In addition, the sample with the narrowest well width exhibited a blueshift of the PL transition energy as a function of the excitation power between square and cubic root laws. To explain these experimental observations, quantized energies in SLs were calculated using the band structures that were suggested and modified using an established band parameter. The most plausible band structure was revealed by comparing experimental observations with the calculations. PL from the SL samples was found to occur within the GaAsSb well (type I) in between the gamma point (Γ) of the conduction band and the heavy hole (HH) energy level in the valence band. To understand the underlying causes of the blueshift phenomenon, a self-consistent calculation that solves the Schrödinger and Poisson equations was performed iteratively as a function of carrier density. As a result, the blueshift of transition energy with an increase in the carrier density was confirmed in the type-I transition between Γ and HH bands if the lowest transition was type II between L for AlAsSb and HH for GaAsSb bands. The Hartree potential due to the separately confined electrons and holes in the SLs slightly narrowed the GaAsSb well width by modifying the conduction band.

Effective local potentials for density and density-matrix functional approximations with non-negative screening density.

A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. 136, 224109 (2012)]. As illustrated, a convenient variational quantity in that approach is the "screening" or "electron repulsion" density, ρrep, corresponding to the local, KS Hartree, exchange and correlation potential through Poisson's equation. Two constraints, applied to this minimization, largely remove self-interaction errors from the effective potential: (i) ρrep integrates to N - 1, where N is the number of electrons, and (ii) ρrep ≥ 0 everywhere. In this work, we introduce an effective "screening" amplitude, f, as the variational quantity, with the screening density being ρrep = f2. In this way, the positivity condition for ρrep is automatically satisfied, and the minimization problem becomes more efficient and robust. We apply this technique to molecular calculations, employing several approximations in DFT and in reduced density matrix functional theory. We find that the proposed development is an accurate, yet robust, variant of the constrained effective potential method.

On accelerating a multilevel correction adaptive finite element method for Kohn-Sham equation

Based on the numerical method proposed in Hu et al. (2018) [22] for Kohn-Sham equation, further improvement on the efficiency is obtained in this paper by i). designing a numerical method with the strategy of separately handling the nonlinear Hartree potential and exchange-correlation potential, and ii). parallelizing the algorithm in an eigenpairwise approach. The feasibility of two approaches is analyzed in detail, and the new algorithm is described completely. Compared with previous results, a significant improvement of numerical efficiency can be observed from plenty of numerical experiments, which make the new method more suitable for the practical problems.

Role of electron-electron interaction in the plasmon modes of twisted bilayer graphene

The unconventional properties of magic angle twisted bilayer graphene (TBG), such as correlated insulator states and superconductivity, have drawn significant attention to areas where electron-electron interactions play an important role. However, the role of electron-electron interactions on the plasmon properties of TBG has rarely been studied. In this study, we focus on TBG with a twist angle near the magic angle (1.32 \ifmmode^\circ\else\textdegree\fi{}), and examine the plasmon and optical absorption properties using the continuum model involving Hartree potentials that describe the electron-electron interaction. We find that the Hartree potentials decrease the energy of the intraband plasmon due to the band flattening driven by the interaction between electrons, whereas the energy of the interband plasmon is slightly increased by the Hartree potentials. Moreover, the splitting of the interband absorption peak occurs due to the effects of the Hartree potentials, which can be verified in experiments. Interestingly, the ultrahigh wave location (${\ensuremath{\lambda}}_{\mathrm{air}}/{\ensuremath{\lambda}}_{p}\ensuremath{\sim}2000$) of the intraband plasmon enables TBG to be a superior platform for future terahertz optoelectronic devices.

Atomistic Hartree theory of twisted double bilayer graphene near the magic angle

Twisted double bilayer graphene (tDBLG) is a moiré material that has recently generated significant interest because of the observation of correlated phases near the magic angle. We carry out atomistic Hartree theory calculations to study the role of electron–electron interactions in the normal state of tDBLG. In contrast to twisted bilayer graphene, we find that such interactions do not result in significant doping-dependent deformations of the electronic band structure of tDBLG. However, interactions play an important role for the electronic structure in the presence of a perpendicular electric field as they screen the external field. Finally, we analyze the contribution of the Hartree potential to the crystal field, i.e. the on-site energy difference between the inner and outer layers. We find that the on-site energy obtained from Hartree theory has the same sign, but a smaller magnitude compared to previous studies in which the on-site energy was determined by fitting tight-binding results to ab initio density-functional theory (DFT) band structures. To understand this quantitative difference, we analyze the ab initio Kohn–Sham potential obtained from DFT and find that a subtle interplay of electron–electron and electron–ion interactions determines the magnitude of the on-site potential.

Formulation of temperature dependent effective Hartree potential incorporating quadratic over linear molecular DOFs-surface modes couplings and its effect on quantum dynamics of D2 (v = 0, j = 0)/D2 (v = 0, j = 2) on Cu(111) metal surface

The effect of surface temperature on the scattering and dissociation processes of D2 (v = 0, j = 0)/D2 (v = 0, j = 2) on Cu(111) metal plane is investigated by formulating a time and temperature dependent effective Hamiltonian within mean-field approach, where the molecular degrees of freedom and surface mode vibrations are assumed to be weakly coupled with each other. While constructing such effective Hamiltonian with a Hartree product type wavefunction, we incorporate: (i) an operator algebra method to circumscribe higher order-quadratic (anharmonic) molecular DOFs-surface modes couplings over the linear coupling case implemented previously [Adhikari and coworkers, J. Chem. Phys. 154, 104103 (2021)]; (ii) surface temperature by considering Bose–Einstein or Maxwell–Boltzmann probability factors for the initial state distribution of the surface vibrational modes. Finally, a six-dimensional (6D) quantum dynamical (QD) calculation is performed with such newly formulated effective Hartree potential and calculated transition/dissociation probabilities at various surface temperature situations. The quadratic (anharmonic) molecular DOFs-surface modes couplings modify the reaction and transition probabilities substantially with change of surface temperature, which indicates the crucial role of surface mode vibrations on the molecule-surface scattering phenomena.

Electron mobility in asymmetric GaN/AlGaN quantum well transistor structure: effect of alloy disorder scattering

We analyze the electron mobility μ of GaN/AlGaN based quantum well (QW) transistor structure. We consider the potential profile V(z) by including the potential due topolarization (V p ) and Hartree potential (V H ) owing to surface electron density N s . The low temperature mobility is governed by the alloy disorder (ad-) and interface roughness (ir-) scatterings. As N s increases, μ increases. However, for larger N s (N s > 0.6 × 1013 cm−2), there is a deviation showing decreasing trend of μ. We show that the ad- scattering plays a vital role in governing μ. An increase in N s causes narrowing of the polarization induced channel potential through V H and hence facilitates the larger extension of the subband wave function into the surface barrier. Accordingly, the ad-scattering increases, thereby reducing μ. we show that with an increase in well width there is a substantial rise in μ in quantum well (QW) structures while almost no change in μ in double heterostructures (DH). Enhancement of height of the barriers leads to different results, i.e., for the back barrier, there is a reduction in μ in both QW and DH structures, while for the surface barrier, there is a rise in μ. The fascinating trends of our results of μ in different GaN/AlGaN structures elucidate the importance of ad-scattering on low temperature μ.

Fundamental Aspects of Semiconductor Device Modeling Associated With Discrete Impurities: Monte Carlo Simulation Scheme

We discuss the theoretical basis of the Boltzmann transport equation (BTE) and the Monte Carlo (MC) simulation scheme to take into account the discrete nature of impurities in semiconductor substrates. This is achieved by explicitly considering the self-consistent coupling between the BTE and Poisson’s equation and by separating the impurity potential into long- and short-range parts in those equations. We show that the Hartree potential is represented by the long-range part of the potential, whereas the scattering potential for the BTE is naturally derived within the framework, rather than an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> assumption. The proposed scheme is validated by showing that MC simulations with discrete impurities in bulk can reproduce the conventional simulation results with the “jellium” impurity. Also, by including both static and dynamic potential fluctuations, the MC simulation can predict the correct mobility even under discrete impurities.

Effect of external electric field on photo-responsivity of CdS/ZnSe multiple quantum well photodetector

We show the enhancement of photo-responsivity through applied external electric field F of CdS/ZnSe multiple quantum well (MQW) photo-detector for the detection of mid infrared wavelengths. The subband energy levels E n are calculated using the Schrödinger equation via finite difference method by incorporating exchange-correlation potential and Hartree potential caused by doping in the well layer. We note that by increasing F , E n and the corresponding optical transition energies decreases. It is observed that dipole matrix element M 21 reduces for higher F and we obtain approximately 38 % lower value of M 21 at F = 40 kV/cm. Moreover, absorption coefficient decreases with F due to the strong dependence on M 21 . We obtain current density of 0.03 A/cm 2 and responsivity of 0.012 A/W at wavelength λ = 2.73 μm for M (number of wells) = 20, well width L w = 2 nm at F = 20 kV/cm. We show that the responsivity is enhanced by increasing M, L w as well as doping concentration N D in the well. We also achieved higher photo-responsivity in CdS/ZnSe MQW using our proposed model as compared to the earlier reported results for GaAs/AlGaAs QWIP . • We achieved enhancement of photo-responsivity in CdS/ZnSe QWIP as a function of electric field ( F ). • The Photocurrent ( J ) and Responsivity ( R ) are more significant at higher F . • Enhnacement of J and R with F is due to the reduction in dipole matrix element. • Increasing doping concentrations, number of wells and well widths of QWIP enhances responsivity.

Direct observation of resonant tunneling in heterostructure with a single quantum well

A resonant-tunneling conductivity was experimentally registered in a doped heterostructure with a single quantum well using admittance spectroscopy. Earlier, this effect was only realized in artificially created resonant tunneling structures, having four heterojunctions. A heterostructure with an In0.3Ga0.7As/GaAs quantum well was examined in the temperature range of 10–300 K. In admittance spectra, a competition of thermionic and tunneling escape mechanisms was noticed with a non-exponential Arrhenius plot. By means of numerical self-consistent simulations in a quantum box, we have shown the role of a quasi-bound level in resonant tunneling of electrons; in addition, the energies and wave functions of the quasi-bound state were derived in dependence on an applied bias. The modification of a transparency coefficient for a two-barrier Hartree potential as a function of the quantum well width and in dependence on the applied bias was also calculated. The resonant state took place only at symmetric barriers and disappeared, when the electric field tilted the barriers. The results can be used to develop a new type of resonant tunneling diodes and as a method for diagnostics of the tunnel effect in semiconductors.

Computing with DFT Band Offsets at Semiconductor Interfaces: A Comparison of Two Methods.

Two DFT-based methods using hybrid functionals and plane-averaged profiles of the Hartree potential (individual slabs versus vacuum and alternating slabs of both materials), which are frequently used to predict or estimate the offset between bands at interfaces between two semiconductors, are analyzed in the present work. These methods are compared using several very different semiconductor pairs, and the conclusions about the advantages of each method are discussed. Overall, the alternating slabs method is recommended in those cases where epitaxial mismatch does not represent a significant problem.

Exchange-mediated mutual correlations and dephasing in free-electrons and light interactions

The quantum world distinguishes itself from the classical world by being governed by probability amplitudes rather than probabilities. On a single-particle level, quantum phases can be manipulated leading to observable interference patterns that can be used as a probe e.g. in matter wave microscopy. But the quantum world bears even more fascinating effects when it comes to the interplay between more than one particle. Correlations between quantum particles such as entanglement can be exploited to speed up computational algorithms or enable secure cryptography. Here, we propose and numerically explore a thought experiment to address the question whether quantum correlations between particles can be used in matter wave microscopy. Specifically, we address the following questions: can information be transferred between two mutually spin-correlated free-electron wavepackets? Can Coulomb and exchange correlations be linked to the decoherence and dephasing mechanisms of matter waves? Using a time-dependent Hartree–Fock algorithm, we will show that the exchange term has a substantial role in transferring the information between two mutually spin-correlated electrons, whereas the Hartree potential (or mean-field Coulomb potential) dominates the dephasing on a single-particle level. Our findings might facilitate fermionic matter wave interferometry experiments designed to retrieve information about non-classical correlations and the mechanism of decoherence in open quantum systems.

Detection of DNA Bases via Field Effect Transistor of Graphene Nanoribbon With a Nanopore: Semi-Empirical Modeling.

DNA sequencing techniques are critical in order to investigate genes' functions. Obtaining fast, accurate, and affordable DNA bases detection makes it possible to acquire personalized medicine. In this article, a semi-empirical technique is used to calculate the electron transport characteristics of the developed z-shaped graphene device to detect the DNA bases. The z-shaped transistor consists of a pair of zigzag graphene nanoribbon (ZGNR) connected through an armchair graphene nanoribbon (AGNR) channel with a nanopore where the DNA nucleobases are positioned. Non-equilibrium Green's function (NEGF) integrated with semi-empirical methodologies are employed to analyze the different electronic transport characteristics. The semi-empirical approach applied is an extension of the extended Hückel (EH) method integrated with self-consistent (SC) Hartree potential. By employing the NEGF+SC-EH, it is proved that each one of the four DNA nucleobases positioned within the nanopore, with the hydrogen passivated edge carbon atoms, results in a unique electrical signature. Both electrical current signal and transmission spectrum measurements of DNA nucleobases inside the device's pore are studied for the different bases with modification of their orientation and lateral translation. Moreover, the electronic noise effect of various factors is studied. The sensor sensitivity is improved by using nitrogen instead of hydrogen to passivate the nanopore and by adding a dual gate to surround the central semiconducting channel of the z-shaped graphene nanoribbon.