Band Spin-orbit Splitting Research Articles

Spin-orbit splittings and energy band gaps calculated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

We assess the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the calculation of spin-orbit (SO) splittings and energy band gaps. We have employed a set of 23 semiconductors with available experimental data, including group IV elements, and group III-V, II-VI, and IB-VII compounds. The spin-orbit interaction is included in the calculations using relativistic effective core potentials within a second-variation approximation. HSE errrors are similar to those obtained previously without including SO in the calculation and using a weighted average of the SO split bands for the reference value [J. Chem. Phys. 123, 174101 (2005)]. Here we explicitly show that the same good agreement remains after explicitly including SO interaction in the calculations and comparing directly to experimental energy band gaps.

Large Bychkov-Rashba spin-orbit coupling in high-mobilityGaN∕AlxGa1−xNheterostructures

We present low temperature magnetoconductivity measurements of a density-tunable and high mobility two-dimensional electron gas confined in the wide bandgap GaN/AlGaN system. We observed pronounced anti-localization minima in the low-field conductivity, indicating the presence of strong spin-orbit coupling. Density dependent measurements of magnetoconductivity indicate that the coupling is mainly due to the Bychkov-Rashba mechanism. In addition, we have derived a closed-form expression for the magnetoconductivity, allowing us to extract reliable transport parameters for our devices. The Rashba spin-orbit coupling constant is $\alpha_{so}$ $\sim$ 6$\times$ 10$^{-13}$eVm, while the conduction band spin-orbit splitting energy amounts to $\Delta_{so}$ $\sim$ 0.3meV at n$_e$=1$\times10^{16}$m$^{-2}$.

First-principles study of the electronic structure of heavy fermionYbRh2Si2

The electronic properties of YbRh2Si2 are studied by means of band structure calculations based on thedensity functional theory within the LDA (local density approximation),LDA+U, and fully relativistic scheme. The 4f derived bands are studied within a relativisticframework which yields flat and spin–orbit split bands, and a correlated band method(LDA+U) that includes correlation corrections. In both cases the uppermost4f band is located roughly 150 meV below the Fermi energyEF, and hybridizes weakly with the dispersive Rh 4d bands and a Rh4dxy band that does not disperse perpendicular to the Rh layers. When weapplied the fully relativistic scheme, the 4f derived bands split intoj = 7/2 and 5/2 excitations due to spin–orbit coupling effects. Thef7/2 multiplet is locatedmuch closer to EF, hybridizing anisotropically with a Rh 4d derived conductionband. This mixing induces a non-integer occupation of the f levelsnf and hencereveals that YbRh2Si2 is a mixed-valence heavy fermion. The 4f electrons can be delocalized through the hybridization withconduction electrons. And the hybridization between f and conduction d electrons plays a importantrole in YbRh2Si2. The Fermi surface splits into three different non-touching sheets. There are two tinycylinder Fermi surfaces around Z points which are from the Rh 4d bands and the largerFermi surfaces are from the 4f derived bands.

Composition and carrier-concentration dependence of the electronic structure of InyGa1−yAs1−xNx films with nitrogen mole fraction of less than 0.012

The electronic structure of Si-doped InyGa1−yAs1−xNx films on GaAs substrates, grown by nitrogen-plasma-assisted molecular-beam epitaxy, was examined by photoreflectance (PR) spectroscopy at temperatures between 20 and 300K. The films were approximately 0.5μm thick and had nitrogen mole fraction between x=0.0014 and x=0.012, measured indirectly by a secondary-ion-mass spectrometry calibration; indium mole fraction between y=0.052 and y=0.075, measured by electron-dispersive x-ray spectroscopy; and carrier concentration between 2×1016 and 1.1×1018cm−3, measured by Hall effect. Three critical-point transitions were identified by PR: the fundamental band gap (highest valence band to the lowest conduction band); the spin-orbit split valence band to the lowest conduction band; and the highest valence band to a nitrogen impurity band (above the lowest conduction band). The measured critical-point energies were described by a band anticrossing (BAC) model with the addition of a Burstein-Moss band-filling term. The fitted BAC parameters were similar to previously reported values. The N impurity level was located 0.3004±0.0101eV above the conduction-band edge at 20K and 0.3286±0.0089eV above the conduction-band edge at 295K. The BAC interaction parameter was 2.588±0.071eV. From the small magnitude of the Burstein-Moss energy shift with increasing carrier concentration, it was inferred that the carrier concentration probed by PR is reduced from the bulk (Hall-effect) carrier concentration by a reduction factor of 0.266±0.145. The PR lines broadened with increasing carrier concentration; the line broadening tracked the predicted Burstein-Moss energy shift for the bulk carrier concentration. The surface-normal lattice constants of the films were measured by x-ray diffraction. Comparison of the measured lattice constants with Vegard’s law showed the presence of tensile strain (in the surface-normal direction) with magnitude between 1.5×10−3 and 3.0×10−3. The effect of strain on the PR energies was too small to observe.

Spin-orbit coupling with ultrasoft pseudopotentials: Application to Au and Pt

We show how to include the spin-orbit coupling in electronic structure calculations of crystalline solids based on plane waves and ultrasoft pseudopotentials. The spin-orbit split electronic band structures of fcc-Au and of fcc-Pt are calculated by fully relativistic pseudopotentials derived from an atomic Dirac-like equation. The results are compared with accurate all-electron calculations available in the literature.

Universal intrinsic spin Hall effect.

We describe a new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. We argue that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening.

Valence band structures and optical transitions of Ga 1− xIn xN yAs 1− y/GaAs compressively strained quantum wells

The electronic structures of the Ga 1− x In x N y As 1− y /GaAs compressively strained quantum wells (QW) are investigated using 6×6 k·p Hamiltonian including the heavy hole, light hole and spin–orbit splitting band. The curves of dependence of transition energy on well width and N mole fraction are obtained. The valence subband energy dispersion curves, density of state and TE and TM squared optical transition matrix elements of three possible QW structures for emitting 1.3 μm wavelength are given.

Electronic band structures of GaInNAs/GaAs compressive strained quantum wells

The electronic structures of the Ga1−xInxNyAs1−y/GaAs compressive strained quantum wells are investigated using 6×6 k⋅p Hamiltonian including the heavy hole, light hole, and spin-orbit splitting band. By varying the well width and mole fraction of N in the well material, the effects of quantum confinement and compressive strain are examined. The curves of dependence of transition energy on well width and N mole fraction are obtained. The valence subband energy dispersion curves and TE and TM squared optical transition matrix elements of three possible quantum well structures for emitting 1.3 μm wavelength are given.

First-principles elastic constants and electronic structure ofα−Pt2Siand PtSi

We have carried out a first-principles study of the elastic properties and electronic structure for two room-temperature stable Pt silicide phases, tetragonal $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Pt}}_{2}\mathrm{Si},$ and orthorhombic PtSi. We have calculated all of the equilibrium structural parameters for both phases: the a and c lattice constants for $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Pt}}_{2}\mathrm{Si}$ and the a, b, and c lattice constants and four internal structural parameters for PtSi. These results agree closely with experimental data. We have also calculated the zero-pressure elastic constants, confirming prior results for pure Pt and Si and predicting values for the six (nine) independent, nonzero elastic constants of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Pt}}_{2}\mathrm{Si}$ (PtSi). These calculations include a full treatment of all relevant internal displacements induced by the elastic strains, including an explicit determination of the dimensionless internal displacement parameters for the three strains in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Pt}}_{2}\mathrm{Si}$ for which they are nonzero. We have analyzed the trends in the calculated elastic constants, both within each material as well as among the two silicides and the pure Pt and Si phases. The calculated electronic structure confirms that the two silicides are poor metals with a low density of states at the Fermi level, and consequently we expect that the Drude component of the optical absorption will be much smaller than in good metals such as pure Pt. This observation, combined with the topology found in the first-principles spin-orbit split band structure, suggests that it may be important to include the interband contribution to the optical absorption, even in the infrared region.

Rigorous hole band structure calculations of p-type δ-doping superlattices in silicon

Self-consistent hole band structure calculations are performed for p-type δ-doped quantum wells and superlattices (SLs) in Si by solving the six-band Luttinger–Kohn effective mass equations, together with Poisson equation, in a plane-wave representation. Non-parabolicities due to couplings between heavy, light, and spin–orbit split bands are fully taken into consideration. Exchange and correlation effects within the multicomponent hole gas are included in the local density approximation. Results are presented for hole band structures, Fermi levels, and potentials for p-type δ-doping SLs, in which the acceptor sheet doping concentration and SL period were varied. Our results are compared with the available experimental data.

P-typeδ-doping quantum wells and superlattices in Si: Self-consistent hole potentials and band structures

The hole-subband and -miniband structures of periodically acceptor $\ensuremath{\delta}$-doped quantum wells and superlattices (SL's) in silicon are calculated self-consistently within the effective-mass theory and the local-density approximation. The full six-band Luttinger-Kohn effective-mass equations are solved, together with Poisson equation, in a plane-wave representation. Nonparabolicities due to couplings between heavy, light, and spin-orbit split bands are fully taken into consideration. To account for exchange and correlation (XC) effects within the multicomponent hole gas, a parametrized expression for the XC potential energy is adopted. Hole band structures, Fermi levels, and potentials are presented for a series of p-type $\ensuremath{\delta}$-doping SL's, varying the acceptor doping concentrations, periods, and doping spreads. The inclusion of the spin-orbit split band is reflected essentially in nonparabolicities, and it starts to play an important role already for intermediate concentrations. For acceptor doping concentrations above $1.1\ifmmode\times\else\texttimes\fi{}{10}^{14} {\mathrm{cm}}^{\ensuremath{-}2},$ the split-off band is populated for SL periods in both SL and isolated well regimes. A comparison with the available experimental data shows fairly good agreement. Particularly, the data reported on admittance and infrared spectroscopies can be reasonably interpreted if one assumes indirect transitions between subbands, as is the case in p-type $\ensuremath{\delta}$-doped GaAs.

Photoluminescence studies of excitonic transitions in GaN epitaxial layers

GaN epitaxial layers on sapphire substrates were grown by the rotating disk metal organic chemical vapor deposition technique. Excitonic transitions from conduction band to spin-orbit split valence bands were observed. At 12 K we observed donor bound exciton and a very weak acceptor bound exciton. The temperature dependence of luminescence peak positions of free-excitons A and B were fitted to the Varshni’s equation to study the variation of the band gap with temperature. The linewidth of the free exciton (A) was studied as a function of temperature and was explained by theoretical model considering the scattering of excitons with acoustic phonons and longitudinal optical phonons. In the 12 K spectrum we also observed phonon-assisted excitonic transitions. The activation energy of the free exciton (A) was found to be 26 meV, while that of the donor bound exciton was 7 meV. The binding energy of the donor was estimated as 35 meV and that of the acceptor as 250 meV. The band gap of GaN was found to be 3.505 eV at 12 K and 3.437 at room temperature. All the parameters obtained in the present investigation are compared with those reported in the literature.

Hole band structure of p-type delta-doping quantum wells in silicon

The subband structure of p-type delta-doping wells in Si is calculated within self-consistent six-component envelope function theory, taking the heavy hole, light hole and spin-orbit split bulk bands into account. The subband dispersion shows a pronounced anticrossing behavior, being enhanced by the small splitting between heavy and light hole levels and the strong subband anisotropy parallel to the doping layers. For sheet doping concentrations above 1013 cm−2, subbands derived from the spin-orbit split band compete with heavy and light hole subbands. A comparison with experimental results shows good agreement.

Electronic structures of the zinc-blende GaN/Ga 1− xAl xN compressively strained superlattices and quantum wells

The electronic structures of the zinc-blende GaN/Ga 0.85Al 0.15N compressively strained superlattices and quantum wells are investigated using a 6×6 Hamiltonian model (including the heavy hole, light hole and spin-orbit splitting band). The energy bands, wavefunctions and optical transition matrix elements are calculated. It is found that the light hole couples with the spin-orbit splitting state even at the k=0 point, resulting in the hybrid states. The heavy hole remains a pure heavy hole state at k=0. The optical transitions from the hybrid valence states to the conduction states are determined by the transitions of the light hole and spin-orbit splitting states to the conduction states. The transitions from the heavy hole, light hole and spin-orbit splitting states to the conduction states obey the selection rule Δ n=0. The band structures obtained in this work will be valuable in designing GaN/GaAlN based optoelectronic devices.

A photoemission study of the bandstructure of InSb (100)

Angle resolved photoemission spectroscopy with synchrotron radiation was used to study the valence band structure of InSb (100). Normal emission energy distribution curves exhibit direct transitions from the valence band maximum Γ8 at the Γ-point of the Brillouin zone and along the [100] direction (Δ). The splitting of the valence band maximum along Δ into a heavy hole band Δ5(hh) and a light hole band Δ5(lh) is clearly resolved. The amount of the splitting is found to be < 200 meV. In addition, we find transitions from the spin-orbit split valence band Γ7. The valence band spin-orbit splitting at the Γ-point is determined to be (750 ± 50) meV. The dispersion behaviour of light and heavy hole bands and the spin-orbit split valence band as well as the resulting data for spin-orbit and light-hole/heavy-hole-band splitting of the topmost valence bands are compared to band structures calculated by nonlocal pseudopotential and self-consistent local-density approximations.

A photoemission study of the bandstructure of InSb (100)

Angle resolved photoemission spectroscopy with synchrotron radiation was used to study the valence band structure of InSb (100). Normal emission energy distribution curves exhibit direct transitions from the valence band maximum Γ 8 at the Γ-point of the Brillouin zone and along the [100] direction (Δ). The splitting of the valence band maximum along Δ into a heavy hole band Δ 5(hh) and a light hole band Δ 5(lh) is clearly resolved. The amount of the splitting is found to be < 200 meV. In addition, we find transitions from the spin-orbit split valence band Γ 7. The valence band spin-orbit splitting at the Γ-point is determined to be (750 ± 50) meV. The dispersion behaviour of light and heavy hole bands and the spin-orbit split valence band as well as the resulting data for spin-orbit and light-hole/heavy-hole-band splitting of the topmost valence bands are compared to band structures calculated by nonlocal pseudopotential and self-consistent local-density approximations.

Optical gain in zinc-blende [formula omitted] strained quantum well laser

Based on the valence subbands of the zinc-blende GaN Ga 0.85Al 0.15N strained quantum wells obtained by a 6×6 Hamiltonian (including heavy hole, light hole and spin-orbit splitting band), optical gain and radiative current density are calculated for the strained quantum well laser structures. The compressive strain in the GaN well region strongly depresses the TM mode optical gain and enhances the TE mode optical gain.

Valence subband structures of wurtzite GaN/AlGaN quantum wells

Valence subband structures of wurtzite GaN/AlGaN quantum wells have been studied, using the k⋅p method in which the parameters are derived by first-principles calculations. Since wurtzite GaN and AlN have the small spin-orbit splitting energies (≤20 meV), the mixing among the six bands including the spin-orbit split band should be considered to obtain the subband states correctly. According to our parameters for the GaN/AlGaN quantum well, the hole carrier confinement in the two-dimensional systems does not lead to a significant reduction of hole masses, and so the threshold current density of wurtzite GaN/AlGaN quantum well laser diodes is not decreased.

Uniaxial stress study of the quantum transitions in a strained layer (001) In 0.21Ga 0.79As/GaAs single quantum well

We have studied the effects of large, external uniaxial stress ( T) along [100] and [110] on the optical properties of a strained layer (001) In 0.21Ga 0.79As/GaAs single quantum well (SQW). Because of the large stresses employed the observed energy shifts exhibit a nonlinear behavior due to the stress-induced coupling with the spin-orbit split band. For T ∥[110] the piezoelectric coupling produces an electric field along [001] which has a significant effect on both the energies and intensities of the various intersubband transitions.

Spin-resolved photoemission from epitaxial Au layers on Pt(111): Coverage dependence of the bandstructure and evidence of surface resonances

Au/Pt(111) has been studied by spin-, angle- and energy-resolved photoemission with normal incident circularly polarized synchrotron radiation of BESSY and normal photoelectron emission for different Au coverages. The prepared layers were characterized by LEED and Augerelectron spectroscopy and turned out to grow up two dimensional and epitaxially. In the photoemission experiments the development of the 3-dimensional bandstructure in the Λ-direction could be observed. For a coverage of 2.6 layers the highest occupied spin-orbit split bands are located at about 0.6 eV lower binding energy than the corresponding bands for a 3D-Au crystal and show dispersion which is, however, weaker than in a 3D-Au crystal. A 5 layer Au adsorbate was found to have already the same dispersion and energetic location as a Au(111)-crystal. For thick gold layers, which behave in photoemission like Au(111)-crystals, we find structures that cannot be due to direct transitions into a free electron like final band. The coverage dependence and spin polarization of these structures show that some of them are due to surface resonances, while the origin of one strong peak could not yet be explained conclusively. In addition we find strong hybridization and two avoided crossings in the occupied part of the bandstructure.