Electronic Eigenvalues Research Articles

PyArc: A python package for computing absorption and radiative coefficients from first principles

Light absorption and radiative recombination are two critical processes in optoelectronic materials that characterize the energy conversion efficiency. The absorption and radiative coefficients are thus key properties for device optimization and design. Here, we develop a python package named pyArc that allows rigorous computation of absorption and radiative coefficients from first principles. By integrating several interpolation strategies to augment k-point sampling in reciprocal space, our code is accurate yet highly efficient. In addition to evaluation of the coefficients, our code is capable of intuitive analysis of carrier distribution, facilitating a deeper understanding of the microscopic mechanisms underlying the radiative coefficients. Utilizing GaAs as a prototypical example, we demonstrate how to employ our package to compute absorption and radiative coefficients and to investigate the key features in the electronic structure that give rise to these coefficients. Program SummaryProgram title: PyArcCPC Library link to program files:https://doi.org/10.17632/5x9g9bvhcv.1Licensing provisions: MIT licenseProgramming language: Python 3Nature of problem: Light absorption and radiative recombination processes in semiconductors critically impact the energy conversion efficiency of optoelectronic devices. Developing a method to calculate coefficients of the two processes based on first-principles theory is essential, which not only can help to obtain the key properties of those semiconductor materials and guide the device design, but also can unveil the underlying microscopic mechanisms.Solution method: PyArc, written in the Python language, implements first-principles methodologies for the computation of absorption and radiative coefficients of semiconductors based on Fermi's golden rule. This package takes the electronic eigenvalues and dipole matrix elements of a material computed from first-principles codes such as VASP as input. Dense k-point sampling for the Brillouin zone is achieved through efficient interpolation schemes implemented in our code to acquire well converged results. The functionality of cross-sectional visualization of carrier distribution in our code provides intuitive insights into the fundamental mechanism beneath the charge-carrier radiative recombination process.

Electron-vibrational renormalization in fullerenes through ab initio and machine learning methods.

The effect of nuclear vibrations on the electronic eigenvalues and the HOMO-LUMO gap is known for several kinds of carbon-based materials, like diamond, diamondoids, carbon nanoclusters, carbon nanotubes and others, like hydrogen-terminated oligoynes and polyyne. However, it has not been widely analysed in another remarkable kind which presents both theoretical and technological interest: fullerenes. In this article we present the study of the HOMO, LUMO and gap renormalizations due to zero-point motion of a relatively large number (163) of fullerenes and fullerene derivatives. We have calculated this renormalization using density-functional theory with the frozen-phonon method, finding that it is non-negligible (above 0.1 eV) for systems with relevant technological applications in photovoltaics and that the strength of the renormalization increases with the size of the gap. In addition, we have applied machine learning methods for classification and regression of the renormalizations, finding that they can be approximately predicted using the output of a computationally cheap ground state calculation. Our conclusions are supported by recent research in other systems.

Canonical mean-field molecular dynamics derived from quantum mechanics

Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature theab initiomolecular dynamics potential energy is based on the ground state electron eigenvalue problem and the accuracy has been proven to beO(M-1), provided the first electron eigenvalue gap is sufficiently large compared to the given temperature andMis the ratio of nuclei and electron masses. For higher temperature eigenvalues corresponding to excited electron states are required to obtainO(M-1) accuracy and the derivations assume that all electron eigenvalues are separated, which for instance excludes conical intersections. This work studies a mean-field molecular dynamics approximation where the mean-field Hamiltonian for the nuclei is the partial traceh := Tr(He−βH)/Tr(e−βH) with respect to the electron degrees of freedom andHis the Weyl symbol corresponding to a quantum many body Hamiltonian ̂H. It is proved that the mean-field molecular dynamics approximates canonical quantum correlation observables with accuracyO(M-1+tϵ2), for correlation timetwhereϵ2is related to the variance of mean value approximationh. Furthermore, the proof derives a precise asymptotic representation of the Weyl symbol of the Gibbs density operator using a path integral formulation. Numerical experiments on a model problem with one nuclei and two electron states show that the mean-field dynamics has similar or better accuracy than standard molecular dynamics based on the ground state electron eigenvalue.

Electrodynamics of a mesoscopic Möbius quantum wire

Microscopic response theory is used to study the linear electromagnetics of a Möbius jellium quantum wire. In the energy range of interest ( ℏ ω ∼ 1 − 200 m e V ), the wire can be considered as a Möbius band with complete transverse electron confinement ( ∼ one-level quantum well with width w ∼ k F − 1 ≪ λ = c / ω ). The electronic energy eigenvalues and eigenstates are calculated numerically via a diagonalization of a scalar determinant in which the relevant matrix elements of the geometrical potential (given in terms of string curvature and torsion) occur. The exact lowest lying states for a 50 nm long heavily doped GaAs wire are compared to those obtained in lowest-order perturbation theory. The sequence (from the bottom) EOEEOEOO… of the even (E) and odd (O) parity states is not the even–odd sequence EOEOEOEO… of a harmonic potential. The interchanges originate in the peak structure of the geometrical potential. Significant energy splitting of the lowest lying eigenvalues of the Möbius wire is observed when compared to the degenerate energy eigenvalues of a corresponding circular wire. The frequency dependence of the conductivity tensor components are calculated, and the peak structure is identified from the E → E , and O → O and E ↔ O transitions. It is shown that elastic light scattering might be a versatile probe for determining the Möbius wire’s electronic-state structure.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. I. Formalism.

Analytic gradients of electronic eigenvalues require one calculation per nuclear geometry, compared to at least 3n + 1 calculations for finite difference methods, where n is the number of nuclei. Analytic nonadiabatic derivative coupling terms (DCTs), which are calculated in a similar fashion, are used to remove nondiagonal contributions to the kinetic energy operator, leading to more accurate nuclear dynamics calculations than those that employ the Born-Oppenheimer approximation, i.e., that assume off-diagonal contributions are zero. The current methods and underpinnings for calculating both of these quantities, gradients and DCTs, for the State-Averaged MultiReference Configuration Interaction with Singles and Doubles (MRCI-SD) wavefunctions in COLUMBUS are reviewed. Before this work, these methods were not available for wavefunctions of a relativistic MRCI-SD Hamiltonian. Calculation of these terms is critical in successfully modeling the dynamics of systems that depend on transitions between potential energy surfaces split by the spin-orbit operator, such as diode-pumped alkali lasers. A formalism for calculating the transition density matrices and analytic derivative coupling terms for such systems is presented.

Plane wave methods for quantum eigenvalue problems of incommensurate systems

We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problems of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our algorithm directly discretizes the eigenvalue problems under the framework of a plane wave method. The emerging ergodicity and the interpretation from higher dimensions give rise to many unique features compared to what we have been familiar with in the periodic systems. The numerical results of 1D and 2D quantum eigenvalue problems are presented to show the reliability and efficiency of our algorithm. Furthermore, the extension of our algorithm to full Kohn-Sham density functional theory calculations is discussed.

Near-infrared light controlling using the photonic crystal with coupled quantum dots in defect layer

We propose a multilayer structure with an active region consisting coupled semiconductor quantum dots to modulate a near-infrared optical probe. The vertically aligned arrays of two quantum dots are simulated to obtain the electron and hole energy eigenvalues. The inter-dot electron and hole tunneling along with coupling laser field are considered to investigate the optical properties of the quantum dot molecules via density matrix method. Probe field transmission through the designed one dimensional photonic crystal, with composed quantum dot molecules defect layer, is monitored. The necessary values of the controlling parameters, i.e. tunneling strength, coupling field intensity and its relative phase with respect to the probe signal for operating in different ON/OFF and amplified-ON regimes are determined. The dynamical response of the quantum dot molecules is also investigated to obtain the switching time between these three regimes. The obtained results confirm that the proposed structure can operate as an optical switch or amplifier in communication technology.

Canonical Quantum Observables for Molecular Systems Approximated by Ab Initio Molecular Dynamics

It is known that ab initio molecular dynamics based on the electron ground-state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low compared to the first electron eigenvalue gap. This work proves that a certain weighted average of the different ab initio dynamics, corresponding to each electron eigenvalue, approximates quantum observables for any temperature. The proof uses the semiclassical Weyl law to show that canonical quantum observables of nuclei–electron systems, based on matrix-valued Hamiltonian symbols, can be approximated by ab initio molecular dynamics with the error proportional to the electron–nuclei mass ratio. The result covers observables that depend on time correlations. A combination of the Hilbert–Schmidt inner product for quantum operators and Weyl’s law shows that the error estimate holds for observables and Hamiltonian symbols that have three and five bounded derivatives, respectively, provided the electron eigenvalues are distinct for any nuclei position and the observables are in the diagonal form with respect to the electron eigenstates.

Efficient Solution of the Electronic Eigenvalue Problem Using Wavepacket Propagation.

We report how imaginary time wavepacket propagation may be used to efficiently calculate the lowest-lying eigenstates of the electronic Hamiltonian. This approach, known as the relaxation method in the quantum dynamics community, represents a fundamentally different approach to the solution of the electronic eigenvalue problem in comparison to traditional iterative subspace diagonalization schemes such as the Davidson and Lanczos methods. In order to render the relaxation method computationally competitive with existing iterative subspace methods, an extended short iterative Lanczos wavepacket propagation scheme is proposed and implemented. In the examples presented here, we show that by using an efficient wavepacket propagation algorithm the relaxation method is, at worst, as computationally expensive as the commonly used block Davidson-Liu algorithm, and in certain cases, significantly less so.

Energy Spectrum of Relativistic Electrons Channeled Through Single-Wall Carbon Nanotubes

The energy eigenvalues of the channeled electrons through single wall carbon nanotubes (n,m) was calculated. According to the continuum model approximation given by Lindhard for the case of an axial channeling in single crystals, the actual periodic potential of a row of atoms is replaced by a potential averaged over a direction parallel to the row, called continuum potential. The calculations was executed by using the atomic interaction potential as given by Moliere potential. The maximum number of bound states and the energy eigenvalues is calculated for positrons of 100 MeV energy incident in a direction parallel to the nanotube axis, by using WKB method. The calculations showed that the effect of temperature by using Debye approximation of thermal vibration amplitude on the channeling potential is very small and gave the same eigenvalues and the same number of bound states as that for the static nanotubes.

Electronic Structure Problem of Alkaline Earth Metals

Purpose: The present study is to resolve the problem in electronic structure of alkaline earth metals bydifferent calculations and conceptual theories. Methodological concept: All discovered alkaline earth metals occur in nature. Experiments have beenconducted to attempt the synthesis of element 120, the next potential member of the group, but they have allmet with failure. The electronic structure of alkaline earth metals determines all their physical properties.Effective electron Eigen value problem of the singly charged alkaline earth metal ion with a single valenceelectron. This valence electron moves in one particle model potential to reproduce the valence excitationenergies of the monocation. Results: The radial degree of freedom of the electronic wave function in a finite element basis set from thesolution of the one electron problem. Using the Lanczos-based package ARPACK, we calculate-for eachvalid combination of angular momentum quantum numbers l and j-the first 18 eigen functions outside thecore shells. In other words, solutions associated with inner shells are skipped. Thus, the selected valence-electron solutions display correct nodal behavior.

Perspective: Methods for large-scale density functional calculations on metallic systems.

Current research challenges in areas such as energy and bioscience have created a strong need for Density Functional Theory (DFT) calculations on metallic nanostructures of hundreds to thousands of atoms to provide understanding at the atomic level in technologically important processes such as catalysis and magnetic materials. Linear-scaling DFT methods for calculations with thousands of atoms on insulators are now reaching a level of maturity. However such methods are not applicable to metals, where the continuum of states through the chemical potential and their partial occupancies provide significant hurdles which have yet to be fully overcome. Within this perspective we outline the theory of DFT calculations on metallic systems with a focus on methods for large-scale calculations, as required for the study of metallic nanoparticles. We present early approaches for electronic energy minimization in metallic systems as well as approaches which can impose partial state occupancies from a thermal distribution without access to the electronic Hamiltonian eigenvalues, such as the classes of Fermi operator expansions and integral expansions. We then focus on the significant progress which has been made in the last decade with developments which promise to better tackle the length-scale problem in metals. We discuss the challenges presented by each method, the likely future directions that could be followed and whether an accurate linear-scaling DFT method for metals is in sight.

EvArnoldi: A New Algorithm for Large-Scale Eigenvalue Problems.

Eigenvalues and eigenvectors are an essential theme in numerical linear algebra. Their study is mainly motivated by their high importance in a wide range of applications. Knowledge of eigenvalues is essential in quantum molecular science. Solutions of the Schrödinger equation for the electrons composing the molecule are the basis of electronic structure theory. Electronic eigenvalues compose the potential energy surfaces for nuclear motion. The eigenvectors allow calculation of diople transition matrix elements, the core of spectroscopy. The vibrational dynamics molecule also requires knowledge of the eigenvalues of the vibrational Hamiltonian. Typically in these problems, the dimension of Hilbert space is huge. Practically, only a small subset of eigenvalues is required. In this paper, we present a highly efficient algorithm, named EvArnoldi, for solving the large-scale eigenvalues problem. The algorithm, in its basic formulation, is mathematically equivalent to ARPACK ( Sorensen , D. C. Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations ; Springer , 1997 ; Lehoucq , R. B. ; Sorensen , D. C. SIAM Journal on Matrix Analysis and Applications 1996 , 17 , 789 ; Calvetti , D. ; Reichel , L. ; Sorensen , D. C. Electronic Transactions on Numerical Analysis 1994 , 2 , 21 ) (or Eigs of Matlab) but significantly simpler.

Quantum oscillations and wave packet revival in conical graphene structure

We present analytical expressions for the eigenstates and eigenvalues of electrons confined in a graphene monolayer in the presence of a disclination. The calculations are performed in the continuum limit approximation in the vicinity of the Dirac points, solving Dirac equation by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearence of Aharonov-Bohm oscillation and find out the conditions of gapped and gapless states in the spectrum. We show that the gauge field due to a disclination lifts the orbital degeneracy originating from the existence of two valleys. The broken valley degeneracy has a clear signature on quantum oscillations and wave packet dynamics.

Calibration of ⁵⁷Fe Mössbauer constants by first principles.

Electron density and eigenvalues of the 3 × 3 matrix of the electric field gradients at the (57)Fe nuclei positions have been evaluated with the periodic ab initio CRYSTAL code for a wide range of crystalline compounds, adopting different computational approaches (Hartree-Fock, gradient corrected and hybrids functionals). The robust calibration procedure, involving experimental isomer shifts and quadrupolar splittings, yields reliable Mössbauer parameters, i.e. the isomer shift constant (α) and the nuclear quadrupolar moment (Q). Dependence of the results on the Hamiltonian is explored and well suited localized basis sets for periodic calculations are provided.

The linear and nonlinear optical properties of an off-center hydrogenic donor impurity in nanowire superlattices: Comparison between arrays of spherical and cylindrical quantum dots

Nanowire superlattices (NWSLs) are objects with a wide range of potential applications in nanoscale electronics and optics. In this paper, we consider an off-center hydrogenic donor impurity in two different NWSL with cylindrical cross-section which involved an array of spherical or cylindrical quantum dots (QDs) along their axis and called Sph and Cyl NWSLs, respectively. The electronic eigenstates and energy eigenvalues of NWSLs are determined by applying finite difference method. Additionally, optical properties such as linear, nonlinear and total intersubband absorption coefficients (ACs) and refractive index (RI) changes are investigated by means of compact density matrix approach. The results show that (I) optical ACs and RI changes of a Sph NWSL are smaller than those of Cyl NWSL. (II) The amplitudes of ACs and RI changes are strongly affected by impurity position and show an oscillatory behavior as the impurity shifts away from the center. (III) Resonance condition in optical spectrum can be adjusted by shape of QDs and impurity position and both blue and red shifts are appeared in ACs as the impurity shifts away from the center of NWSLs. (IV) Total optical absorption saturation intensity can be controlled by the shape of QDs or the impurity position. Moreover, optical incident intensities correspond to the saturation in optical spectrum in Cyl NWSL are smaller than their values for Sph NWSL and have a minimum values as the impurity is located at the center of barriers for both Sph and Cyl NWSLs. (V) By increasing the relaxation time the amplitude of the total AC will increase and for large values of relaxation time a saturation appears in optical spectrum which strongly depends on the Al concentration, impurity position and type of NWSL.

Rectifying properties of oligo(phenylene ethynylene) heterometallic molecular junctions: molecular length and side group effects.

The rectifying properties of α,ω-dithiol terminated oligo(phenylene ethynylene) molecules sandwiched between heterometallic electrodes, including the molecular length and side group effects, are theoretically investigated using the fully self-consistent nonequilibrium Green's function method combined with density functional theory. The results show nonlinear variation with changes in molecule length: when the molecule becomes longer, the current decreases at first and then increases while the rectification shifts in the opposite direction. This stems from the change in molecular eigenstates and the coupling between the molecule and electrodes caused by different molecular lengths. The rectifying behavior of heterometallic molecular junctions can be attributed to the asymmetric molecule-electrode contacts, which lead to asymmetric electronic tunneling spectra, molecular eigenvalues, molecular orbitals, and potential drop at reversed equivalent bias voltages. Our results provide a fundamental understanding of the rectification of heterometallic molecular junction, and a prediction of rectifiers with different rectification properties from those in the experiment, using electrodes with reduced sizes.

Mapped Finite Element Discrete Variable Representation

Efficient numerical solver for the Schrödinger equation is very important in physics and chemistry. The finite element discrete variable representation (FE-DVR) was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 (2000)] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 3Σg+ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.

AlGaN/GaN-based HEMT on SiC substrate for microwave characteristics using different passivation layers

In this paper, a new gate-recessed AlGaN/GaN-based high electron mobility transistor (HEMT) on SiC substrate is proposed and its DC as well as microwave characteristics are discussed for Si3N4 and SiO2 passivation layers using technology computer aided design (TCAD). The two-dimensional electron gas (2DEG) transport properties are discussed by solving Schrodinger and Poisson equations self-consistently resulting in various subbands having electron eigenvalues. From DC characteristics, the saturation drain currents are measured to be 600 mA/mm and 550 mA/mm for Si3N4 and SiO2 passivation layers respectively. Apart from DC, small-signal AC analysis has been done using two-port network for various microwave parameters. The extrinsic transconductance parameters are measured to be 131.7 mS/mm at a gate voltage of Vgs = −0.35 V and 114.6 mS/mm at a gate voltage of Vgs = −0.4 V for Si3N4 and SiO2 passivation layers respectively. The current gain cut-off frequencies (ft) are measured to be 27.1 GHz and 23.97 GHz in unit-gain-point method at a gate voltage of −0.4 V for Si3N4 and SiO2 passivation layers respectively. Similarly, the power gain cut-off frequencies (fmax) are measured to be 41 GHz and 38.5 GHz in unit-gain-point method at a gate voltage of −0.1 V for Si3N4 and SiO2 passivation layers respectively. Furthermore, the maximum frequency of oscillation or unit power gain (MUG = 1) cut-off frequencies for Si3N4 and SiO2 passivation layers are measured to be 32 GHz and 28 GHz respectively from MUG curves and the unit current gain, ∣ h21 ∣ = 1 cut-off frequencies are measured to be 140 GHz and 75 GHz for Si3N4 and SiO2 passivation layers respectively from the abs ∣ h21 ∣ curves. HEMT with Si3N4 passivation layer gives better results than HEMT with SiO2 passivation layer.

Operator extensions theory model for electromagnetic field–electron interaction

A model of the point-like interaction between the classical electromagnetic field and the quantum electron is suggested. It is based on the theory of self-adjoint extensions of symmetric operators in the Pontryagin and Hilbert spaces. The shift of the electron eigenvalues due to the electromagnetic field influence is obtained.