Spin-orbit Levels Research Articles

InAs/GaAs p-type quantum dot infrared photodetector with higher efficiency

An InAs/GaAs quantum dot infrared photodetector (QDIP) based on p-type valence-band intersublevel hole transitions as opposed to conventional electron transitions is reported. Two response bands observed at 1.5–3 and 3–10 μm are due to transitions from the heavy-hole to spin-orbit split-off QD level and from the heavy-hole to heavy-hole level, respectively. Without employing optimized structures (e.g., the dark current blocking layer), the demonstrated QDIP displays promising characteristics, including a specific detectivity of 1.8×109 cm·Hz1/2/W and a quantum efficiency of 17%, which is about 5% higher than that of present n-type QDIPs. This study shows the promise of utilizing hole transitions for developing QDIPs.

Infrared-active spin-orbit transitions of halogen atom dopants in solid parahydrogen: The role of trapping site geometry

We present theoretical calculations of the (2)P(1/2) ← (2)P(3/2) spin-orbit transition of Cl dopants embedded as substitutional impurities in solid parahydrogen (pH2) matrices. In the lower-energy (2)P(3/2) spin-orbit level, the Cl atom's electron density distribution is anisotropic, and slightly distorts the geometry of the atom's trapping site. This distortion leads to a blue shift in the spin-orbit transition energy; the blue shift is enhanced when we account for the large-amplitude zero point motions of the pH2 molecules surrounding the Cl dopant. We also show that the intensity of the transition depends on the geometry of the trapping site. In the gas phase, the (2)P(1/2) ← (2)P(3/2) atomic transition is electric dipole forbidden. However, when the Cl atom resides in trapping sites that mimic the hexagonal close packed morphology of pure solid pH2, the transition becomes electric dipole allowed through interaction-induced transition dipole moments. These transition dipole moments originate in the anisotropic electron density distribution of the lower-energy (2)P(3/2) spin-orbit level.

Activation of Methane by Os+ : Guided-Ion-Beam and Theoretical Studies.

Activation of methane by the third-row transition-metal cation Os+ is studied experimentally by examining the kinetic energy dependence of reactions of Os+ with CH4 and CD4 using guided-ion-beam tandem mass spectrometry. A flow tube ion source produces Os+ in its electronic ground state and primarily in the ground spin-orbit level. Dehydrogenation to form [Os,C,2 H]+ +H2 is exothermic, efficient, and the only process observed at low energies for reaction of Os+ with methane, whereas OsH+ dominates the product spectrum at higher energies. The kinetic energy dependences of the cross sections for several endothermic reactions are analyzed to give 0 K bond dissociation energies (in eV) of D0 (Os+ C)=6.20±0.21, D0 (Os+ CH)=6.77±0.15, and D0 (Os+ CH3 )=3.00±0.17. Because it is formed exothermically, D0 (Os+ CH2 ) must be greater than 4.71 eV, and a speculative interpretation suggests the exothermicity exceeds 0.6 eV. Quantum chemical calculations at the B3LYP/def2-TZVPP level show reasonable agreement with the experimental bond energies and with previous theoretical values available. Theory also provides the electronic structures of the product species as well as intermediates and transition states along the reactive potential energy surfaces. Notably, the structure of the dehydrogenation product is predicted to be HOsCH+ , rather than OsCH2 + , in contrast to previous work.

The fully quantum state-resolved inelastic scattering of NO(X) + Ne: experiment and theory

Fully Λ-doublet quantum state-resolved differential cross-sections for collisions of NO(X) with neon at a collision energy of 540 cm−1 are presented. Initial state selection of the Ω = 0.5, j = 0.5, f Λ-doublet level of the NO(X) was achieved using hexapole focussing. Both spin-orbit level conserving and spin-orbit level changing transitions have been studied. The experimental results are compared with those obtained from quantum scattering calculations and are shown to be in excellent agreement. Quantum scattering calculations have also been performed on a modified potential energy surface with the attractive region removed, to determine the effects this has on the differential cross-sections. Comparisons are also made with the inelastic scattering of NO(X) with He and Ar.

Ab initio study of ground and excited states of 6Li40Ca and 6Li88Sr molecules

We present quantum-chemical calculations for the ground and some low-lying excited states of isolated LiCa and LiSr molecules using multi-state complete active space second-order perturbation theory (MS-CASPT2). The potential energy curves (PECs) and their corresponding spectroscopic constants, obtained at the spin-free (SF) and spin-orbit (SO) levels, agree well with available experimental values. Our SO-MS-CASPT2 calculation at the atomic limit (R = 100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% for both LiCa and LiSr. In addition, permanent dipole moments and transition dipole moments at the SF level are also obtained. Rovibrational calculations of the ground and selected excited states, together with the spontaneous emission rates, demonstrate that the formation of ultracold LiCa and LiSr molecules in low-lying vibrational levels of the electronic ground state may be possible.

On structure and bonding of lanthanoid trifluorides LnF3 (Ln = La to Lu)

The trends in the series of lanthanoid (lanthanide) trifluoride molecules LnF3 (Ln = La to Lu) are governed by the valence-active Ln(4f,5d,5p,6s) shells. The series is investigated by quasi-relativistic density functional theory at both the scalar and spin-orbit-coupled levels. Integrating many of the previous experimental and theoretical deductions, we obtain the following comprehensive picture: (1) The comparatively small Ln-F bond length contraction of 14 pm from La to Lu is rather smooth but weakly modulated by spin-orbit coupling. (2) From La to Lu the floppy structure becomes more quasi-planar. (3) The heterolytic LnF bond energies (⅓LnF3→⅓Ln(3+) + F(-)) at the spin-orbit averaged level increase smoothly from 15.3 to 16.3 eV for La to Lu, only the 'divalent' lanthanoids Eu and Yb are outliers with 0.2 eV higher bond energies. (4) The homolytic LnF bond energies (⅓LnF3→⅓Ln + F) however show an overall W-shaped double-periodicity with maxima for LaF3, GdF3 and LuF3, decreasing from La to Eu and from Gd to Yb, the large individual variations being caused by different spin-orbit coupling and Coulomb interaction effects in Ln(0) and LnF3. (5) The Ln-F interaction is basically ionic (increasing with decreasing ionic radii) with some dative Ln(3+)← F(-) bonding. (6) The latter is of the Ln(5d)-F(2p) type with a rather constant bond order from La to Lu, with small Ln(5p) and very small Ln(4f) semi-core contributions decreasing from La to Lu. All these trends are rationalized.

Large insulating gap in topological insulators induced by negative spin-orbit splitting

In a cubic topological insulator (TI), there is a band inversion whereby the $s$-like ${\ensuremath{\Gamma}}_{6\mathrm{c}}$ conduction band is below the $p$-like ${\ensuremath{\Gamma}}_{7\mathrm{v}}+{\ensuremath{\Gamma}}_{8\mathrm{v}}$ valence bands by the ``inversion energy'' ${\ensuremath{\Delta}}_{i}l0$. In TIs based on the zinc-blende structure such as HgTe, the Fermi energy intersects the degenerate ${\ensuremath{\Gamma}}_{8\mathrm{v}}$ state so the insulating gap E${}_{g}$ between occupied and unoccupied bands vanishes. To achieve an insulating gap E${}_{g}g0$ critical for TI applications, one often needs to resort to structural manipulations such as structural symmetry lowering (e.g., Bi${}_{2}$Se${}_{3}$), strain, or quantum confinement. However, these methods have thus far opened an insulating gap of only $l$0.1 eV. Here we point out that there is an electronic rather than structural way to affect an insulating gap in a TI: if one can invert the spin-orbit levels and place ${\ensuremath{\Gamma}}_{8\mathrm{v}}$ below ${\ensuremath{\Gamma}}_{7\mathrm{v}}$ (``negative spin-orbit splitting''), one can realize band inversion (${\ensuremath{\Delta}}_{i}l0$) with a large insulating gap (E${}_{g}$ up to 0.5 eV). We outline design principles to create negative spin-orbit splitting: hybridization of $d$ orbitals into $p$-like states. This general principle is illustrated in the ``filled tetrahedral structures'' (FTS) demonstrating via GW and density functional theory (DFT) calculations E${}_{g}g0$ with ${\ensuremath{\Delta}}_{i}l0$, albeit in a metastable form of FTS.

Spectral engineering of LaF3:Ce3+ nanoparticles: The role of Ce3+ in surface sites

Due to the high surface-to-volume ratio, luminescence centers on the surface have relative dominance in the overall spectral response of nanoparticles. The luminescence of LaF3:Ce3+ nanoparticles was investigated in the spectral and temporal domains with a particular focus on the role of Ce3+ on the surface. These nanoparticles present two luminescence bands at 4.10 eV and 4.37 eV attributed to Ce3+ transitions from the 5d level to the spin-orbit split 4f ground levels 2F5/2 and 2F7/2, in addition to a low-energy band at 3.62 eV that has been attributed to Ce3+ ions residing in perturbed sites. The growth of up to three undoped shells, ca. 0.9 nm thick each, around the core promoted a progressive enhancement of luminescence output, concomitant with an increase in the fluorescence lifetime due to the weakening of energy transfer through multipolar interaction between Ce3+ in the core and quenching defects on the surface. Also, the growth of the first shell led to a decrease in the relative intensity of the low-energy band and a 0.23 eV shift to higher energies. These results were interpreted as being due to the existence of two types of perturbed sites, one on the surface that is eliminated by the growth of the first shell, and another within the volume of the nanoparticle, similar to observations in bulk single crystals. This work demonstrates how surface engineering can affect and control the luminescence behavior of this nanomaterial.

M + Ng potential energy curves including spin-orbit coupling for M = K, Rb, Cs and Ng = He, Ne, Ar

The X(2)Σ(1/2)(+), A(2)Π(1∕2), A(2)Π(3∕2), and B(2)Σ(1/2)(+) potential energy curves and associated dipole matrix elements are computed for M + Ng at the spin-orbit multi-reference configuration interaction level, where M = K, Rb, Cs and Ng = He, Ne, Ar. Dissociation energies and equilibrium positions for all minima are identified and corresponding vibrational energy levels are computed. Difference potentials are used together with the quasistatic approximation to estimate the position of satellite peaks of collisionally broadened D2 lines. The comparison of potential energy curves for different alkali atom and noble gas atom combinations is facilitated by using the same level of theory for all nine M + Ng pairs.

Systematic Trends in Non-resonant Inelastic X-ray Scattering of Actinides

ABSTRACTNonresonant inelastic x-ray scattering (NIXS) measurements probing the 5d → 5f electronic transitions at the uranium O4,5 edges in a localized electron system such as UO2 show a good agreement with many-electron atomic spectral calculations. The higher multipole spectra are split into two peaks that can be assigned as the 5d5/2 and 5d3/2 structures, despite the large electrostatic interactions. A new sum rule for the branching ratio of spin-orbit split core levels in electric multipole spectra, which generalizes the sum rule for dipole transitions in x-ray absorption spectroscopy, allows for a systematic analysis of the NIXS spectra. The branching ratio is linearly proportional to the expectation value of the angular part of the spin-orbit interaction in the initial state, where the rank of the multipole determines the coefficient of the linear dependence. This spin-orbit sum rule can be an important diagnostic tool for high-energy spectroscopies.

Relativistic Effect on 77Se NMR Chemical Shifts of Various Selenium Species in the Framework of Zeroth-Order Regular Approximation

The relativistic effects on absolute magnetic shielding tensors (σ(Se)) are explicitly evaluated for various selenium species (40 species) with the DFT(BLYP)-GIAO method. Calculations are performed under relativistic and nonrelativistic conditions with the Slater-type basis sets in ADF 2010 in the framework of ZORA, employing the optimized structures under nonrelativistic conditions at B3LYP of Gaussian 03. Quadruple zeta all electron with four polarization functions (QZ4Pae) are mainly applied to evaluate σ(Se). Ranges of the effect on diamagnetic (σ(d)(Se)), paramagnetic shielding tensors (σ(p)(Se)), and σ(d+p)(Se) (= σ(d)(Se) + σ(p)(Se)) are -24 to -20 ppm, -115 to -3 ppm, and -136 to -26 ppm, respectively. The spin-orbit terms (σ(so)(Se)) are evaluated to be 92-225 ppm with QZ4Pae, which clarifies the effect on total shielding tensors (σ(t)(Se) = σ(d+p)(Se) + σ(so)(Se)) to be -8 to 152 ppm, at the spin-orbit ZORA level. The calculated σ(t)(Se) values reproduced well the observed values.

Site-selected luminescence of atomic europium in the solid rare gases

Site-selective excitation has been used to simplify complex emission recorded in the visible spectral region for atomic europium isolated in the solid rare gases. In addition to y(8)P resonance fluorescence, excitation of the y(8)P state produces emission from the z(6)P state and the metastable a(10)D state. Very weak emission at 690 nm is tentatively assigned to the J = 9/2 level of the z(10)P state. Eu atoms isolated in the red and blue sites exhibit very different temperature dependence both spectrally and temporally. For the y(8)P state emission the red site atoms exhibit small Stokes shifts and yield radiative lifetimes while the emission from the blue site loses intensity and the temporal profiles shorten dramatically between 10 and 16 K indicating very efficient non-radiative relaxation in this site. An analysis of the Stokes shifts exhibited for the y(8)P state in each site supports the attributions made in a previous publication [O. Byrne and J.G. McCaffrey, J. Chem. Phys. 134, 124501 (2011)] that the smaller blue tetravacancy site has a greater repulsive interaction with the guest. With the exception of the y(8)P state resonance fluorescence, the recorded decay profiles of all the other emissions exhibit multiple components. This behaviour has been attributed to the existence of multiple crystal field levels arising from the splitting of the distinct spin-orbit levels from which emission occurs.

Deposition and characterization of layer-by-layer sputtered AgGaSe2 thin films

Sputtering technique has been used for the deposition of AgGaSe2 thin films onto soda-lime glass substrates using sequential layer-by-layer deposition of GaSe and Ag thin films. The analysis of energy dispersive analysis of X-ray (EDXA) indicated a Ga-rich composition for as-grown samples and there was a pronounce effect of post-annealing on chemical composition of AgGaSe2 thin film. X-ray diffraction (XRD) measurements revealed that Ag metallic phase exists in the amorphous AgGaSe2 structure up to annealing temperature 450°C and then the structure turned to the single phase AgGaSe2 with the preferred orientation along (112) direction with the annealing temperature at 600°C. The surface morphology of the samples was analyzed by scanning electron microscopy (SEM) measurements. The structural parameters related to chalcopyrite compounds have been calculated. Optical properties of AgGaSe2 thin films were studied by carrying out transmittance and reflectance measurements in the wavelength range of 325–1100nm at room temperature. The absorption coefficient and the band gap values for as-grown and annealed samples were evaluated as 1.55 and 1.77eV, respectively. The crystal-field and spin-orbit splitting levels were resolved. These levels (2.03 and 2.30eV) were also detected from the photoresponse measurements almost at the same energy values. As a result of the temperature dependent resistivity and mobility measurements in the temperature range of 100–430K, it was found that the decrease in mobility and the increase in carrier concentration following to the increasing annealing temperature attributed to the structural defects (tetragonal distortion, vacancies and interstitials).

Relativistic calculations of ground and excited states of LiYb molecule for ultracold photoassociation spectroscopy studies

We report a series of quantum-chemical calculations for the ground and some of the low-lying excited states of an isolated LiYb molecule by the spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Potential energy curves, spectroscopic constants, and transition dipole moments (TDMs) at both spin-free and spin-orbit levels are obtained. Large spin-orbit effects especially in the TDMs of the molecular states dissociating to Yb((3)P(0,1,2)) excited states are found. To ensure the reliability of our calculations, we test five types of incremental basis sets and study their effect on the equilibrium distance and dissociation energy of the ground state. We also compare CASPT2 and CCSD(T) results for the ground state spectroscopic constants at the spin-free relativistic level. The discrepancies between the CASPT2 and CCSD(T) results are only 0.01 Å in equilibrium bond distance (R(e)) and 200 cm(-1) in dissociation energy (D(e)). Our CASPT2 calculation in the supermolecular state (R=100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% error. Transition dipole moments of the super molecular state (R=100 a.u.) dissociating to Li((2)P) excited states are quite close to experimental atomic TDMs as compared to the Yb((3)P) and Yb((1)P) excited states. The information obtained from this work would be useful for ultracold photoassociation experiments on LiYb.

ChemInform Abstract: Chemistry of Excited Electronic States

Atomic and molecular orbitals are among the tools used by chemists to view the world. The validity of this view for reaction systems can be experimentally probed by examination of the chemistry of electronically excited states and, in particular, by comparison of the reactivities of states having different orbital occupations (electron configurations). Reactivity changes associated with electron configuration are instructive with regard to chemists9 views of molecular orbital interactions, but electronic excitation can also influence the course of a chemical reaction by increasing the energy content of the system or by affecting access to different potential energy surfaces by changing spin, orbital symmetry, or spin-orbit level. These various effects are illustrated by studies of gasphase transition metal—mediated H—H and C—H bond-activation processes.

Luminescence spectroscopy of matrix-isolated atomic manganese: Site size and orbital occupancy dependence of crystal field splitting

Narrow linewidth emission features observed in the near-UV following y (6)P state excitation of atomic manganese isolated in the solid rare gases are assigned to b (4)D and a (4)P states. These states arise from the 3d(5)4s(2) electronic configuration, identical to that of the (6)S ground state, and the origin of the narrow linewidths. Two thermally stable sites, labeled blue and red on the basis of their position in absorption spectra, are occupied by atomic Mn in Ar and Kr while a single site is present in Xe. The red site produces a single, narrow line emission for the b (4)D state at 329 nm. In contrast, a lineshape analysis of the complex blue site b (4)D state emission between 331 and 332 nm reveals the occurrence of three zero phonon lines (ZPLs). Millisecond emission decay curves recorded for these features are found to be complex, requiring double and triple exponential fit functions. The origins of the complex decays and multiple ZPLs are shown to arise from weak crystal field splitting (CFS) of the J=7/2 spin-orbit level of the b (4)D state of atomic Mn isolated in the blue site of the solid rare gases. Fields of cubic symmetry are capable of inducing splitting for J>3/2 so atoms isolated in both single vacancy and tetravacancy sites in the fcc lattices of the solid rare gases are prone to this effect. b (4)D state emission is also produced following y (6)P excitation for Mn atoms occupying the red sites in Ar and Kr. However, Mn atoms isolated in the larger tetravacancy sites have small matrix shifts and do not exhibit any CFS. The magnitudes of the weak CF splittings are shown to depend on both the excited state electronic configurations 3d(5)4s(2) b (4)D and 3d(6)4s(1) a (4)D states and the size of the matrix site occupied by atomic Mn.

Spin relaxation due to deflection coupling in nanotube quantum dots

We consider relaxation of a single-electron spin in a nanotube quantum dot due to its coupling to flexural phonon modes, and identify a new spin-orbit-mediated coupling between the nanotube deflection and the electron spin. This mechanism dominates other spin-relaxation mechanisms in the limit of small energy transfers. Due to the quadratic dispersion law of long-wavelength flexons, $\ensuremath{\omega}\ensuremath{\propto}{q}^{2}$, the density of states $dq/d\ensuremath{\omega}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1/2}$ diverges as $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Furthermore, because here the spin couples directly to the nanotube deflection, there is an additional enhancement by a factor of $1/q$ compared to the deformation-potential coupling mechanism. We show that the deflection coupling robustly gives rise to a minimum in the magnetic field dependence of the spin lifetime ${T}_{1}$ near an avoided crossing between spin-orbit split levels in both the high- and low-temperature limits. This provides a mechanism that supports the identification of the observed ${T}_{1}$ minimum with an avoided crossing in the single-particle spectrum by Churchill et al. [Phys. Rev. Lett. 102, 166802 (2009)].

Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order

The 3.5 post-Newtonian (PN) order is tackled by extending the canonical formalism of Arnowitt, Deser, and Misner to spinning objects. This extension is constructed order by order in the PN setting by utilizing the global Poincare invariance as the important consistency condition. The formalism is valid to linear order in the single spin variables. Agreement with a recent action approach is found. A general formula for the interaction Hamiltonian between matter and transverse-traceless part of the metric at 3.5PN is derived. The wave equation resulting from this Hamiltonian is considered in the case of the constructed formalism for spinning objects. Agreement with the Einstein equations is found in this case. The energy flux at the spin-orbit level is computed.

Effects of the first hydration sphere and the bulk solvent on the spectra of the f2isoelectronic actinide compounds: U4+, NpO2+, and PuO22+

The electronic spectra of the 5f(2) isoelectronic actinide compounds U(4+), NpO(2)(+), and PuO(2)(2+) have been investigated theoretically both in gas phase and in solution. In the latter case the solvent was modelled by a saturated first hydration sphere, five water molecules for NpO(2)(+), and PuO(2)(2+) and eight for U(4+), and a continuum model describing the remaining solvent. The transition energies and oscillator strengths were obtained at the spin-orbit level using the relativistic wave function based multi-configuration methods CASPT2 (complete active space with second-order perturbation theory) and MRCI + DC (Davidson corrected multi-reference configuration interaction), followed by a spin-orbit CI based on a dressed effective spin-orbit Hamiltonian. This study is an attempt to contribute to an enhanced understanding of the electronic structure of tetravalent actinide ions and actinyl(v) and (vi) ions. The spin-orbit MRCI and spin-orbit CASPT2 transitions energies have been compared for the bare ions, leading us to the conclusion that the spin-orbit CASPT2 approach is reasonably accurate and can be used with confidence for the calculation of the hydrated species. The first hydration sphere and the bulk solvent lift degeneracies, but the effect on the transition energies is fairly small for the two actinyl ions, while it is larger, up to several thousands of wave numbers for U(4+). The calculations allowed us to make assignments of the experimentally observed absorption spectra for all species. The computed transition energies and intensities compared favourably with experiment.

Model core potentials for studies of scalar-relativistic effects and spin-orbit coupling at Douglas–Kroll level. I. Theory and applications to Pb and Bi

A theory of model core potentials that can treat spin-orbit-coupling (SOC) effects at the level of Douglas-Kroll formalism has been developed. By storing the damping effect of kinematic operator in the Douglas-Kroll spin-orbit operator into an additional set of basis set contraction coefficients, the Breit-Pauli spin-orbit code in the GAMESS-US program was successfully used to perform Douglas-Kroll spin-orbit calculations. It was found that minute errors in the radial functions of valence orbitals lead to large errors in the spin-orbit energy levels and thus fitting the radial part of the spin-orbit matrix elements is necessary in model core potential parametrization. The first model core potentials that include the new formalism were developed for two 6p-block elements, Pb and Bi. The valence space of the 5p, 5d, 6s, and 6p orbitals was used because of the large SOC between the 5p and 6p orbitals. The model core potentials were validated in the calculations of atomic properties as well as spectroscopic constants of diatomic metal hydrides. The agreement between results of the model core potential and all-electron calculations was excellent, with energy errors of hundreds of cm(-1) and hundredths of eV, r(e) errors of thousandths of A, and omega(e) errors under 20 cm(-1). Two kinds of interplay between SOC effect and bonding process (antibonding and bonding SOC) were demonstrated using spin-free term potential curves of PbH and BiH. The present study is the first extension of the model core potential method beyond Breit-Pauli to Douglas-Kroll SOC calculations.