Ordering Of Energy Levels Research Articles

Effect of conduction band parabolicity on the spectrum and binding energy of a hydrogenic impurity in GaAs spherical quantum dots

The energy levels and binding energies of a hydrogenic impurity in GaAs spherical quantum dots with radius R are calculated by the finite difference method. The system is assumed to have an infinite confining potential well with radius R, which can be viewed as a hard wall boundary condition. The parabolicity of the conduction band profile for GaAs material can be viewed as a parabolic potential well. The energy levels and binding energies are depended dramatically on the radius of the quantum dot and the parabolic potential well. The results show that parabolic potential can remarkably alter the energy level ordering and binding energy level ordering of hydrogenic impurity states for the quantum dot with a smaller radius R.

Экситоны и биэкситоны в сфероидальных квантовых точках А-=SUB=-2-=/SUB=-B-=SUB=-6-=/SUB=-

AbstractIn the limit of strong quantum confinement the lower energy states of excitons and biexcitons in spheroidal quantum dots of semiconductors with a fourfold degenerate vertex of the valence band, which are active in the dipole approximation at one- and two-photon excitation, have been considered. The comparative analysis of the order of energy levels of the hole in the potentials of the infinitely deep quantum well and a three-dimensional harmonic oscillator taking into account the axial anisotropy of the quantum dot (QD) shape is carried out. It is shown that the anisotropy of the QD shape can lead to the opposite sign of splitting with respect to angular momentum projection ±3/2, ±1/2 for spatially odd (1 P _3/2) and even (1 S _3/2) levels of the hole. At the same time, in the case of the potential of an infinitely deep quantum well, an inversion of the order of 1 S _3/2 and 1 P _3/2 levels can be observed at values of the ratio of the effective masses of the light and heavy holes β = m _lh/ m _hh ≈ 0.14. The type of the trial wave functions of the hole for the state 1 P _3/2 in the potential of an isotropic three-dimensional harmonic oscillator depending on β is proposed. The dependence of the binding energy of excitons in the considered potentials on β is presented and the possibility of formation of various biexcitonic states is considered.

Exact ordering of energy levels for one-dimensional interacting Fermi gases with SU (N) symmetry

Based on the exact solution of one-dimensional Fermi gas systems with $SU(n)$ symmetry in a hard wall, we demonstrate that we are able to sort the ordering of the lowest energy eigenvalues of states with all allowed permutation symmetries, which can be solely marked by certain quantum numbers in the Bethe ansatz equations. Our results give examples beyond the scope of the generalized Lieb-Mattis theorem, which can only compare the ordering of energy levels of states belonging to different symmetry classes if they are comparable according to the pouring principle. In the strongly interacting regime, we show that the ordering of energy levels can be determined by an effective spin-exchange model and extend our results to the non-uniform system trapped in the harmonic potential.

Universal Sequence of the Ground States and Energy Level Ordering in Frustrated Antiferromagnetic Rings with a Single Bond Defect

Universal Sequence of the Ground States and Energy Level Ordering in Frustrated Antiferromagnetic Rings with a Single Bond Defect

Sequences of ground states and classification of frustration in odd-numbered antiferromagnetic rings

The sequences of ground states in frustrated antiferromagnetic rings with odd number of local spins characterized by a single bond defect or by arbitrary uniform couplings to an additional spin located at the center are determined. The sequences provide firm constraints on the total ground-state quantum numbers, which are more stringent than those arising from the Lieb-Mattis theorem for bipartite quantum spin systems. Apart from their theoretical importance, they suggest the possibility of tailoring a given class of the molecular nanomagnets with desired ground-state properties by tuning the relevant couplings. In particular, they predict the spin $S=1/2$ ground state for the centered rings composed of the half-integer spins with approximately uniform interactions. They confirm the applicability of the recent classification of spin frustration in both types of molecular nanomagnets. The classification is also discussed in the classical limit for the first class of the rings, providing a direct picture of frustration types. The Lieb-Mattis energy-level ordering and an analog of the Land\'e band, i.e., the energy spectra properties simplifying the characterization of the rings using the bulk magnetic or NMR measurements, are briefly discussed.

Structural Influence on Superatomic Orbitals of Typical Gold Nanostructure Building Blocks

We compared superatomic orbitals mainly contributed by 6s atomic orbitals among spherical core–shell cluster Au13, hexagonal plane Au7 and a (5,5) nanotube segment Au35 through first-principles density functional theory calculations. The compatibility between geometry and orbital morphology influences both the presence and the energy level order of particular superatomic orbitals. Taking Au13 as a reference, which possesses a regular configuration of 1S21P61D5, the hexagonal Au7 in 1S21P41D1 lacks the 1P occupied superatomic orbital which is distributed out of the structural plane. Different from the nearly degenerated five occupied 1D orbitals in Au13, Au35 in 1S21P61D101F101G61H1 shows energy separations over 4.0 eV between split 1D regions and 1F regions according to the preference of tubular geometry to different orbital morphologies. The structural reliance of the electronic structure revealed by these typical building blocks might be informative for bottom-up design and fabrication of nanoscale devices based on a gold nanostructure and contributes to the variety and operability of nanoscale materials.

Effective three-particle forces in polyvalent atoms

We study effective three-particle interactions between valence electrons, which are induced by the core polarization. Such interactions are enhanced when valence orbitals have strong overlap with the outermost core shell, in particular for the systems with partially filled f-shell. We find that in certain cases the three-particle contributions are large, affecting the order of energy levels, and need to be included in high-precision calculations.

Band engineering for surface emission enhancement in Al-rich AlGaN-based deep-ultraviolet light emitting diodes

The optical polarization properties of Al-rich AlGaN/AlN quantum wells (QWs) with different structure parameters were analyzed using the modified theoretical model based on the effective mass equation. It is demonstrated that the optical polarization properties of AlGaN-based QWs are determined by the valence subband structure, including the energy level order and the valence subband coupling. The results show that the TE-polarized emission is enhanced in Al-rich AlGaN/AlN QWs with smaller well width, a buffer layer inducing compressive stress, and a staggered well layer owing to the change in the valence subband structure. Hence, the enhancement of surface emission from deep-ultraviolet (DUV) AlGaN-based light-emitting diodes (LEDs) can be realized by adjusting the QW structure parameters to induce a valence subband change.

Universal sequence of ground states validating the classification of frustration in antiferromagnetic rings with a single bond defect

The sequence of $2s+1$ ground states in the frustrated antiferromagnetic rings with odd number $n$ of local spins $s$ resulting from a single bond defect strength is determined, and occurrence of the Lieb-Mattis energy level ordering, proven for the bipartite systems only, is confirmed for the rings in question. The sequence is universal, provides the theoretical basis for the recent classification of spin frustration in molecular magnets, and indicates that the Lieb-Mattis theorem (LMT) consequences exist for the nonbipartite rings. The states in the sequence are characterized by the total spin $S$ fulfilling the constraint $S\ensuremath{\le}s$ and are separated by $2s$ Kahn degenerate frustration points. The possible LMT consequences in other systems are discussed.

DFT/TDDFT studies of the ancillary ligand effects on structures and photophysical properties of rhenium (I) tricarbonyl complexes with the imidazo[4,5-f]-1,10-phenanthroline ligand

The seven rhenium (I) tricarbonyl complexes having a general formula fac-[ReBr(CO)3(R1,R2,R3-N^N)] (N^N = imidazo[4,5-f]-1,10-phenanthroline; R1 = tBu, R2 = R3 = H, 1; R1 = CCH, R2 = R3 = H, 2; R1 = tBu, R2 = CCH, R3 = H, 3; R1 = tBu, R2 = R3 = CCH, 4; R1 = tBu, R2 = CH3, R3 = H, 5; R1 = tBu, R2 = R3 = CH3, 6; R1 = tBu, R2 = OCH3, R3 = H, 7) have been investigated theoretically by density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods. The different substituted groups on N^N ligand induce changes on the electronic structures and photophysical properties for these complexes. It is found that the introduction of CC decreases the energy level of lowest unoccupied molecular orbital (LUMO) while the introduction of CH3 or OCH3 lead to increase the energy level of LUMO. The order of LUMO energy level rising is in line with the increasing of donating abilities of substituted groups; and the influence of R2 position is greater than that of R1 position on LUMO energy level. The lowest energy absorption bands have changes in the order of 7 < 6 < 5 < 1 < 2 < 3 < 4. These results of electronic affinity (EA), ionization potential (IP), and reorganization energy (λ) indicate that all of these complexes can be used as electron transporting materials. Moreover, the smallest difference between λelectron and λhole of 4 indicates that it is better to be used as an emitter in the organic light-emitting diodes. © 2015 Wiley Periodicals, Inc.

Blue-emitting Eu2+-activated LaOX (X = Cl, Br, and I) materials: crystal field effect.

Novel blue-emitting LaOBr:Eu(2+) and LaOI:Eu(2+) phosphors have been successfully synthesized and compared to LaOCl:Eu(2+). The emission spectra of LaOX:Eu(2+) (X = Cl, Br, and I) show that the peak maxima change somewhat to the red-shift region; 425 nm for LaOCl:Eu(2+), 427 nm for LaOBr:Eu(2+), and 431 nm for LaOI:Eu(2+), which is quite opposite to one based on spectrochemical series (I(-) < Br(-) < Cl(-)). From diffuse reflectance spectra, the band gap energies for LaOCl, LaOBr, and LaOI host lattice are estimated as 5.53 eV (44,594 cm(-1)), 5.35 eV (43,142 cm(-1)), and 4.82 eV (38,868 cm(-1)), respectively, using the Kubelka-Munk function. For LaOX host lattices, the band gap energies are gradually decreased going from Cl to I as the order of energy levels of np orbitals is Cl 3p < Br 4p < I 5p. A quantum wave function calculation from crystal field theory (CFT) indicates the same tendency with experimental data in the LaOX:Eu(2+) (X = Cl, Br, and I) phosphor materials. With considerations of the radial wave function shape, crystral structure differences and electronegativities among phosphor materials, the splitting energies of 5d orbitals are calculaed; ΔECl = 14,597 cm(-1), ΔEBr = 14,864 cm(-1), ΔEI = 15,001 cm(-1) for LaOX:Eu(2+) (X = Cl, Br, and I). It is noteworthy that the crystal field strength decreases when the interatomic distance decreases, which is probably dependent on the ionic radius of halide ions in the series of LaOX:Eu(2+) phosphor materials.

Jet-cooled laser-induced fluorescence spectroscopy of cyclohexoxy: rotational and fine structure of molecules in nearly degenerate electronic States.

The rotational structure of the previously observed B̃(2)A' ← X̃(2)A″ and B̃(2)A' ← Ã(2)A' laser-induced fluorescence spectra of jet-cooled cyclohexoxy radical (c-C6H11O) [ Zu, L.; Liu, J.; Tarczay, G.; Dupré, P; Miller, T. A. Jet-cooled laser spectroscopy of the cyclohexoxy radical. J. Chem. Phys. 2004 , 120 , 10579 ] has been analyzed and simulated using a spectroscopic model that includes the coupling between the nearly degenerate X̃ and à states separated by ΔE. The rotational and fine structure of these two states is reproduced by a 2-fold model using one set of molecular constants including rotational constants, spin-rotation constants (ε's), the Coriolis constant (Aζt), the quenched spin-orbit constant (aζed), and the vibronic energy separation between the two states (ΔE0). The energy level structure of both states can also be reproduced using an isolated-state asymmetric top model with rotational constants and effective spin-rotation constants (ε's) and without involving Coriolis and spin-orbit constants. However, the spin-orbit interaction introduces transitions that have no intensity using the isolated-state model but appear in the observed spectra. The line intensities are well simulated using the 2-fold model with an out-of-plane (b-) transition dipole moment for the B̃ ← X̃ transitions and in-plane (a and c) transition dipole moment for the B̃ ← à transitions, requiring the symmetry for the X̃ (Ã) state to be A″ (A'), which is consistent with a previous determination and opposite to that of isopropoxy, the smallest secondary alkoxy radical. The experimentally determined Ã-X̃ separation and the energy level ordering of these two states with different (A' and A″) symmetries are consistent with quantum chemical calculations. The 2-fold model also enables the independent determination of the two contributions to the Ã-X̃ separation: the relativistic spin-orbit interaction (magnetic effect) and the nonrelativistic vibronic separation between the lowest vibrational energy levels of these two states due to both electrostatic interaction (Coulombic effect) and difference in zero-point energies (kinetic effect).

The Low-Lying Electronic States of Pentacene and Their Roles in Singlet Fission

We present a detailed study of pentacene monomer and dimer that serves to reconcile extant views of its singlet fission. We obtain the correct ordering of singlet excited-state energy levels in a pentacene molecule (E (S1) < E (D)) from multireference calculations with an appropriate active orbital space and dynamical correlation being incorporated. In order to understand the mechanism of singlet fission in pentacene, we use a well-developed diabatization scheme to characterize the six low-lying singlet states of a pentacene dimer that approximates the unit cell structure of crystalline pentacene. The local, single-excitonic diabats are not directly coupled with the important multiexcitonic state but rather mix through their mutual couplings with one of the charge-transfer configurations. We analyze the mixing of diabats as a function of monomer separation and pentacene rotation. By defining an oscillator strength measure of the coherent population of the multiexcitonic diabat, essential to singlet fission, we find this population can, in principle, be increased by small compression along a specific crystal direction.

MRCI study on potential energy curves and spectroscopic properties of HF molecule

The potential energy curves of the low-lying electronic states of Hydrogen fluoride (HF) have been investigated by using multireference configuration interaction (MRCI) approach in combination with cc-pV5Z basis sets for H and aug-cc-pV6Z basis sets for F. Three singlet states (X1Σ+,B1Σ+, 11Δ), two triplet valence states (3ΠV,3ΣV+) and five triplet Rydberg states (3ΣR1+,3ΠR1,3ΔR1,3ΣR1-,3ΠR2) of HF molecular are identified. 3ΠV and 3ΣV+ states are repulsive, the spectroscopic parameters (De, Re, ωe, Be and Te) of the bound states are derived in the present work. We find that the order of energy levels of 3ΣR1+,3ΠR1,3ΔR1 electronic states is different with other literatures, 3ΣR1+ is the lowest in these three states, which undergoes a strongly avoided crossing with the valence state 3ΣV+. The 3ΣR1- state is studied at the first time. In addition, the dipole moments (DM), transition dipole moments (TDM), Einstein coefficients (Aυ′υ″), Franck–Condon factors (qυ′υ″) and radiative lifetime (τυ′) for B1Σ+−X1Σ+ systems are predicted.

Nodal ground states and orbital textures in semiconductor quantum dots

Conventional understanding implies that the ground state of a nonmagnetic quantum mechanical system should be nodeless. While this notion also provides a valuable guidance in understanding the ordering of energy levels in semiconductor nanostructures, there are reports that nodal ground states for holes are possible. However, the existence of such nodal states has been debated and even viewed merely as an artifact of a $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model. Using complementary approaches of both $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ and tight-binding models, further supported by an effective Hamiltonian for a continuum model, we reveal that nodal ground states in quantum dots are not limited to a specific approach. Remarkably, the emergence of nodal hole states at the top of the valence band can be attributed to the formation of orbital vortex textures through competition between the hole kinetic energy and the coupling to the conduction band states. We suggest an experimental test for our predictions of the reversed energy ordering and the existence of nodal ground states. We discuss how our findings and the studies of orbital textures could be also relevant for other materials systems.

Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite and related graphs

We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin- ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and the Clebsch–Gordan machinery needed to deal with the arbitrary spin-s representations of the SU(2) is briefly developed. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.

About the disposition of energy levels

The unique properties of central potential of the form −β e−rrγ were studied using the recently developed critical parameter technique. The particular cases of γ = 0 and γ = −1 yield, respectively, the exponential and Yukawa potentials widely used in atomic, molecular and nuclear physics. We found different behavior of the energy levels of this potential for three different ranges of the value of γ. For γ ⩾ 0 it was found that the energy of bound states with the same principal quantum number N decreases with increasing angular momentum ℓ. The Gaussian and Woods–Saxon potentials also show this behavior. In contrast, for −2 < γ ⩽ −1 increasing ℓ gives a higher energy, resembling the Hulthen potential. However, a potential with −1 < γ < 0 possesses mixed properties, which give rise to several interesting results. For one, the order of energy levels with different quantum numbers is not preserved when varying the parameter β. This leads to a quantum degeneracy of the states, and in fact, for a given value of γ we can find the values βthr for which two energy levels with different quantum numbers coincide. Another interesting phenomenon is the possibility, for some values of γ in this range, for two new energy levels with different quantum numbers to appear simultaneously when β reaches their common critical value.

Enhancement of surface emission in deep ultraviolet AlGaN-based light emitting diodes with staggered quantum wells

The optical polarization properties of staggered AlGaN-AlGaN/AlN quantum wells (QWs) are investigated using the theoretical model based on the k·p method. The numerical results show that the energy level order and coupling relation of the valence subband structure change in the staggered QWs and the trend is beneficial to TE polarized transition compared to that of conventional AlGaN/AlN QWs. As a result, the staggered QWs have much stronger TE-polarized emission than conventional AlGaN-based QWs, which can enhance the surface emission of deep ultraviolet (DUV) light-emitting diodes (LEDs). The polarization control by using staggered QWs can be applied in high efficiency DUV AlGaN-based LEDs.

Note on the One-Dimensional Holstein-Hubbard Model

The one-dimensional Holstein-Hubbard model is studied. We show the uniqueness of the ground state and the ordering of energy levels.

Counterexamples to ferromagnetic ordering of energy levels

The Heisenberg ferromagnet has symmetry group SU(2). The property known as ferromagnetic ordering of energy levels (FOEL) states that the minimum energy eigenvalue among eigenvectors with total spin s is monotone decreasing as a function of s. While this property holds for certain graphs such as open chains, in this note we demonstrate some counterexamples. We consider the spin 1/2 model on rings of length 2n for n = 2, 3, …, 8, and show that the minimum energy among all spin singlets is less than or equal to the minimum energy among all spin triplets, which violates FOEL. This also shows some counterexamples to the “Aldous ordering” for the symmetric exclusion process. We also review some of the literature related to these examples.