scholarly journals Hartree potential dependent exchange functional

2016 ◽  
Vol 145 (8) ◽  
pp. 084110 ◽  
Author(s):  
Lucian A. Constantin ◽  
Eduardo Fabiano ◽  
Fabio Della Sala
Keyword(s):  
Hartree Potential

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

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1581
Author(s):  
José C. Conesa
Keyword(s):  
Significant Problem ◽  
Band Offsets ◽  
Semiconductor Interfaces ◽  
Hartree Potential ◽  
Hybrid Functionals

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.

Zur Diffusionstheorie der Spinteilchen:

1964 ◽  
Vol 19 (3) ◽  
pp. 301-314
Author(s):  
H.-D. Kupatt
Keyword(s):  
Coulomb Potential ◽  
Thomas Fermi ◽  
Hartree Potential

Die Relaxations-Weglängen l0, ln usw. der WALDMANNSchen Diffusionstheorie für Spin-1/2-Teilchen werden numerisch bestimmt für Elektronen der Geschwindigkeiten v/c=0,4; 0,5; 0,6; 0,7; 0,8; 0,9, die an neutralen Atomen der Ordnungszahlen Z=13; 48; 80 elastisch gestreut werden. Als Streupotential wird das exponentiell abgeschirmte COULOMB-Potential V= ( — Z e2/r) ·exp( — λ r) vorausgesetzt; für den Abschirmparameter wird vorgegeben λ/λ2=1,00; 1,16; 1,59; 1,80; 1/λ0 ist die THOMAS—FERMI-Länge der streuenden Atomart. — Der Auswertung zugrunde gelegt wird die 2. BORNSche Näherung des MOTT-Streuoperators für das angeschriebene Atompotential. Wo diese ungenau ist, werden die von SHERMAN vertafelten Morr-Funktionen der Streuung am reinen COULOMB-Feld herangezogen. Die BORN-Näherung für Streuung am abgeschirmten Feld wird dann nur im Kleinwinkelbereich benutzt.Auch für Streuung am THOMAS—FERMI-Potential und am HARTREE-Potential (Z = 80) werden die Relaxations-Weglängen ermittelt.

scholarly journals A tight nonlinear approximation theory for time dependent closed quantum systems

2019 ◽  
Vol 27 (3) ◽  
pp. 141-154
Author(s):  
Joseph W. Jerome
Keyword(s):  
Fixed Points ◽  
Nonlinear Approximation ◽  
Quantum Systems ◽  
Time Dependent ◽  
Projection Operators ◽  
Evolution Operators ◽  
Actual Application ◽  
Hartree Potential ◽  
Dependent Potential ◽  
External Time

Abstract The approximation of fixed points by numerical fixed points was presented in the elegant monograph of Krasnosel’skii et al. (1972). The theory, both in its formulation and implementation, requires a differential operator calculus, so that its actual application has been selective. The writer and Kerkhoven demonstrated this for the semiconductor drift-diffusion model in 1991. In this article, we show that the theory can be applied to time dependent quantum systems on bounded domains, via evolution operators. In addition to the kinetic operator term, the Hamiltonian includes both an external time dependent potential and the classical nonlinear Hartree potential. Our result can be paraphrased as follows: For a sequence of Galerkin subspaces, and the Hamiltonian just described, a uniquely defined sequence of Faedo–Galerkin solutions exists; it converges in Sobolev space, uniformly in time, at the maximal rate given by the projection operators.

Self-consistent perturbation treatment of impurities and imperfections in metals

1961 ◽  
Vol 261 (1304) ◽  
pp. 119-133 ◽  
Keyword(s):  
Free Electron ◽  
Plane Waves ◽  
Present Theory ◽  
Bloch Wave ◽  
Perturbation Series ◽  
Order Method ◽  
First Order ◽  
Hartree Potential ◽  
Self Consistent ◽  
First Order Method

A full perturbation treatment of the Dirac density matrix is developed as a basis for selfconsistent calculations in free-electron metals containing localized defects. The present perturbation series is shown to sum to the well-known result for the case of slowly varying potentials. To first order in perturbation theory, exact self-consistent results for the radial density of displaced charge and the Hartree potential in the presence of point singularities have been obtained over a density range sufficient to cover all metals under normal conditions. The basic limitations of Mott’s first-order method, based on the assumption of slowly varying potentials, are shown to be completely removed and the self-consistent density and potential display long-range oscillations. Finally, the application of the present approach to Bloch wave functions rather than plane waves is briefly considered. Friedel’s generalized first-order method, applicable to a band structure, may be obtained from the present theory for sufficiently slowly varying potentials. Unfortunately, such an assumption is seen by comparison with the free-electron findings to lead to serious errors.

Theory of spin-orbit coupling in atoms I. Derivation of the spin-orbit coupling constant

1962 ◽  
Vol 270 (1340) ◽  
pp. 127-143 ◽  
Keyword(s):  
Exact Expression ◽  
Orbit Coupling ◽  
Tensor Operator ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Coupling Constant ◽  
Hartree Fock ◽  
Operator Form ◽  
Hartree Potential

An exact expression for the spin-orbit coupling constant is derived within the Hartree-Fock description of the atom by considering the two body mutual spin-orbit interaction between electrons. The interaction is rewritten in tensor operator form and the contribution of outer electron-core interactions to the coupling constant is calculated. We find that the usual expression < 3F/r8r > where V is the Hartree potential is only approximate, and that certain exchange type terms, which arise because we are dealing with a two-body interaction and determinantal wave function, must also be included. These exchange terms are not simply related to the ordinary electrostatic exchange. The resulting expression for the spin-orbit coupling constant is given in terms of radial integrals which can be calculated using Hartree or Hartree—Fock wave functions. We also discuss the effective magnetic Hamiltonian to be used for the calculation of matrix elements within an atomic configuration.

scholarly journals Electron Mobility in an Unintentionally Doped GaN/AlGaN Surface Quantum Well

2012 ◽  
Vol 21 (4) ◽  
pp. 309
Author(s):  
Nguyen Viet Minh
Keyword(s):  
Quantum Well ◽  
Quantum Wells ◽  
Electron Mobility ◽  
Theoretical Study ◽  
Electron Gas ◽  
Dimensional Electron ◽  
Total Electron ◽  
Hartree Potential ◽  
Self Consistent ◽  
Dimensional Electron Gas

We present a theoretical study the two-dimensional electron gas 2DEG at low temperature in an unintentionally doped GaN/AlGaN surface quantum well, taking adequate account of the roughness-induced scattering mechansms and effect due to sheet polarization charges.  Within model of surface quantum wells 2DEG be described by an extended Fang-Howard wave function, we are able to derive an analytic expression for the self-consistent Hartree potential. Thus, we obtained simple expresion describing the enhancement of the 2DEG screening and unscreened\break potentials for different scattering sources. We studied the electron mobility due to different scattering sources and the total electron mobility in an unintentionally doped GaN/AlGaN surface quantum well.

Formation of a Bound State in the Presence of Repulsive Interaction

2003 ◽  
Vol 17 (18n20) ◽  
pp. 3242-3250 ◽  
Author(s):  
J. D. Fan ◽  
Y. M. Malozovsky
Keyword(s):  
Triplet State ◽  
Multiple Scattering ◽  
Singlet State ◽  
Effective Interaction ◽  
Bound State ◽  
Repulsive Interaction ◽  
Triplet States ◽  
Hartree Potential ◽  
Singlet And Triplet States ◽  
T Matrix

We have examined the effective interaction of two fermions in terms of the T-matrix and shown that there are two different series of ladder diagrams in describing the effective interaction: (1) the exchange ladder diagrams giving rise to the T-matrix for the triplet state with poles for attractive interaction and (2) the Hartree ladder diagrams describing the multiple scattering on the Hartree potential and producing the T-matrix for the singlet state with poles for repulsive interaction. It is verified that a bound state of two fermions in the singlet state exists only in the presence of repulsive interaction between them. We further argue that the potential in the Schrodinger equation should be spin-dependent to describe both the singlet and triplet states.

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