Spin-related phenomena in InAs/GaSb quantum wells

We have studied theoretically the influence of symmetry breaking mechanisms: structural inversion asymmetry, bulk inversion asymmetry, relativistic and non-relativistic interface Hamiltonian and warping on spin split of levels ΔE and optical absorption of linearly polarized light in asymmetrical quantum wells made from zincblende materials grown on [001] direction. The AlSb/InAs/GaSb/AlSb broken-gap quantum wells with hybridized electron-hole states sandwiched by the AlSb barriers have been considered. We have obtained substantial contributions of these effects into the absolute values of spin split of electron and hole states and spinflip optical transitions for the initial state in-plane wave vectors along low symmetry directions such as [12].     

Design issues of 1.55 µm emitting GaInNAs quantum dots

We present a theoretical study of the optical properties of GaInNAs quantum dot (QD) structures, emitting at 1.55 µm wavelength. The theoretical model is based on a 10 × 10 k · p band-anti-crossing Hamiltonian, incorporating valence, conduction and nitrogen-induced bands. We have investigated the influence of the nitrogen to the conduction band mixing, and piezoelectric field on the ground state optical matrix element. For QDs grown on GaAs substrate with a reduced amount of indium and an increased amount of nitrogen in the QD the e _x polarized optical matrix element becomes on the average larger and less sensitive to the variation of both the QD shape and size than is the case of an InNAs QD. For the QD grown on InP substrate the dominant optical dipole matrix element is of the e _z light polarization. Our results identify the specific In and N content in the QDs required for optimal long-wavelength emission on both substrates.     

Electrodynamic features of anisotropic hard superconductors

The low-frequency electromagnetic response of superconducting plates characterized by strong anisotropy of current-carrying capacity in the plane of the sample is studied experimentally and theoretically. Measurements are made on polycrystalline textured plates of the Y-123 system with the c axis lying in the plane of the sample and on a single crystal with a single preferred direction of twinning boundaries. It is shown that the shape of the curves describing the dependence of the relative losses q on the ac field amplitude h ₀ is quite sensitive to the orientation of vector h ₀ in the sample plane. As in the case of isotropic samples, the q(h ₀) dependence is characterized by a single size peak if vector h ₀ is oriented along one of the principal symmetry directions of the anisotropic critical current density. If h ₀ deviates considerably from principal directions, two size peaks are observed on the q(h ₀) curve. A detailed analysis of the evolution of the q(h ₀) curves upon a rotation of vector h ₀ in the sample plane is carried out.     

Transverse zeeman effect for ions in uniaxial crystals with and without mirror plane symmetry

Intra-configuration electric dipole transitions may occur for an ion in a crystal at a site that is not a center of inversion. When an external magnetic field is directed perpendicularly to the principal crystal symmetry axis c, intensity variations in the optical spectrum due to transitions between Zeeman states may appear as the crystal is rotated about c or as the direction of polarization of the incident light is changed with respect to the Zeeman field direction. The electric dipole selection rules giving rise to these intensity fluctuations are derived by consideration of Earney's mirror plane symmetry, and are shown to be identical to those obtained by other means.     

Local field corrections in trigonal Se

The inverse dielectric tensor ?^-1₀₀(q) in the static limit isevaluated in crystalline Se along two symmetry directions, by using a proper model Hamiltonian describing the covalent bond and modified sp³ orbitals as basis states. By comparing the results in diagonal approximation with these obtained including the off diagonal elements (ODE) of the dielectric matrix (DM) it is found that the local field corrections are very large and essential to reproduce the experimental dielectric tensor.     

Magnetic and magneto-optical properties of epitaxial cobalt films grown on a corrugated CaF<Subscript>2</Subscript>/Si surface

The magnetic properties of CaF₂/Co/CaF₂(110)/Si(001) heterostructures fabricated by molecular-beam epitaxy and having a corrugated CaF₂ buffer surface were studied. The optical and magneto-optical properties of these structures reflect the C _2v symmetry of the corrugated structure surface. The studies of hysteresis loops using the longitudinal and transverse magneto-optical Kerr effects under oblique light incidence and of magneto-optical phenomena under near-normal light incidence demonstrate that the corrugated structure surface leads to optical and magneto-optical anisotropies. The magnetization of such structures occurs via coherent magnetization rotation over a wide magnetic-field range. The magnetic anisotropy of these structures is described using a Gaussian distribution of easy axes of magnetization in cobalt granules about the direction parallel to the groove direction. The asymmetry of hysteresis loops of the rotation of the plane of polarization detected under oblique and normal light incidence is shown to be related to the contributions to the effective film permittivity that are quadratic in the magnetic moment.     

Nuclear magnetic resonance in noncollinear antiferromagnet Mn3Al2Ge3O12

The ⁵⁵Mn nuclear magnetic resonance spectrum of noncollinear 12-sublattice antiferromagnet Mn₃Al₂Ge₃O₁₂ has been studied in the frequency range of 200–640 MHz in the external magnetic field H ‖ [001] at T = 1.2 K. Three absorption lines have been observed in fields less than the field of the reorientation transition H _c at the polarization h ‖ H of the rf field. Two lines have been observed at H > H _c and h ⊥ H. The spectral parameters indicate that the magnetic structure of manganese garnet differs slightly from the exchange triangular 120-degree structure. The anisotropy of the spin reduction and (or) weak antiferromagnetism that are allowed by the crystal symmetry lead to the difference of ≈3% in the magnetization of sublattices in the field H < H _c. When the spin plane rotates from the orientation perpendicular to the C ₃ axis to the orientation perpendicular to the C ₄ axis, all magnetic moments of the electronic subsystem decrease by ≈2% from the average value in the zero field.     

Electronic structure of QD arrays: application to intermediate-band solar cells

Intermediate band solar cells (IBSC) have been proposed as a potential design for the next generation of highly efficient photo-voltaic devices. Quantum nanostructures, such as quantum dots (QD), arranged in super-lattice (SL) arrays produce a mini-band (IB) that is separated by a region of zero density of states from other states in the conduction band. Additional absorption from the valence band to the IB and IB to the conduction band allows two photons with energies below the energy gap to be harvested in generating one electron-hole pair. We present a theoretical study of the electronic and optical properties of the IB formed by an InAs/GaAs QD array. The calculations are based on an 8-band k · p Hamiltonian, incorporating mixing between valence and conduction states, strain and piezoelectric field. Theoretical results of the the mini-band width variation with the period of the QD array in the z direction are presented. For one particular spacer distance, d _z = 4 nm, we report detailed variation of the optical dipole matrix elements through the mini-band and identify the character of the states involved. This approach captures the essential physics of the absorption processes in a realistic model of the IBSC structure and will be used to provide input parameters for predictive modelling of transport properties.     

Giant optical anisotropy in M-plane GaN/AlGaN quantum wells due to crystal-field effect

The optical polarization of GaN/AlGaN wurtzite quantum wells in various orientations is studied using an arbitrarily-oriented [hkil] Hamiltonian potential matrix. The optical matrix elements in the wurtzite quantum wells are calculated using the k⋅p finite difference scheme. The results reveal the presence of giant in-plane optical anisotropy (polarized normal to [0001]) in the M-plane (i.e., the -oriented layer plane) GaN/Al_0.2Ga_0.8N quantum well, due to the positive crystal-field split energy effect (ΔCR>0). The present theoretical results are consistent with the photoluminescence measurements presented in the literature [B. Rau, et al., Appl. Phys. Lett. 77 (2000) 3343].     

EPR study of Gd3+ in a ferroelastic BiVO4 single crystal

Electron paramagnetic resonance of the Gd³⁺ ion in a ferroelastic BiVO₄ single crystal with a single domain, grown by the Czochralski method, has been investigated at room temperature using a Q-band spectrometer. The rotation patterns of the resonance fields measured in the crystallographic planes are analyzed using a monoclinic spin Hamiltonian. The principal Z-axis of the second-order zero-field splitting tensorD is found to be along the crystallographicb-axis. Spin Hamiltonian parameters together with the principal axes ofg andD tensors in the monoclinic plane show that the local site symmetry of Gd³⁺ ion in BiVO₄ crystal is monoclinic and that the Gd³⁺ ion substitutes for Bi³⁺ ion.     

Polarization selection rules for the allowed optical transitions in europium-terbium double activated calcium tungstate phosphor

The paper is devoted to the problem of the optical anisotropy of the rare-earth ions occupying low-symmetry positions in crystals. The crystal field multiplets arising from LSJ terms of Eu³⁺ and Tb³⁺ ions in the crystal field of calcium tungstate scheelite (CaWO₄) are analyzed (S₄ point symmetry). The selection rules, in particular, polarization rules for the allowed electric dipole optical transitions in the electronic shells of the Eu³⁺ and Tb³⁺ in CaWO₄ host lattice are discussed. Special attention is paid to the study of the angular (polarization) dependence of the two-photon absorption that seems to be an effective tool for the understanding of the complicated optical pattern. The peculiarities of the anisotropy of the two-photon absorption prove to be specific for each allowed dipole transition in S₄ symmetry center.     

Quantum Mechanical Virial Theorem in Systems with Translational and Rotational Symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G,H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J ², J _z and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.     

Polarization dependence of angle-resolved photoemission spectroscopy of graphite

We have used variable polarization synchrotron radiation to map the valence band electronic structure of graphite by angle-resolved photoemission spectroscopy (ARPES). The experimental results with two orthogonal linear polarization of light signifies the contribution of either even or odd symmetry with respect to the crystal mirror plane towards the photoemission intensity. The σ₁ and σ₂ valence bands show odd reflection symmetry while the π valence band shows even symmetry with respect to the mirror plane. The measured ARPES spectrum using left and right circular polarized lights shows asymmetry in intensity around M point of the Brillouin zone, which ultimately mimicking different partial wave character of σ₁ and σ₃ bands.     

Giant growth-plane optical anisotropy in wurtzite InN/GaN disk-in-wire structures

Using a combination of valence force-field molecular mechanics, 20-band sp³d⁵s^∗ atomistic tight-binding approach, and appropriate post-processing tools, we have studied the origin and nature of optical polarization anisotropy in semiconducting GaN/InN/GaN disk-in-wire structures having wurtzite crystal symmetry and varying InN disk thicknesses. True atomistic symmetry due to the presence of strong internal fields, coupled with quantum mechanical size quantization effects, results in unconventional characteristics in the electronic structure related to non-degeneracy in the excited P states and rotation (symmetry lowering) in the wavefunctions. The optical polarization ratio projected on the XY (growth) plane and, in particular, the transition rates have been shown to be strongly dependent on the crystal internal fields and the thickness of the InN disk.     

Influence of the degenerate d level and of the Jahn-Teller effect on the manganite electronic structure calculated in the tight-binding approximation

E(k) dispersion curves for the charge carriers in the LaMnO₃-like perovskites were calculated for the basic types of canted antiferromagnetic ordering of the Mn sublattice in the framework of the tight-binding approximation. The E(k) spectrum of the antiferromagnetic structures was calculated for the first time taking into account the degeneracy of the Mn e _g level and the Jahn-Teller distortion of the cubic perovskite structure. This calculation involved diagonalization of the 8×8 Hamiltonian matrix. Analytical expressions for the E(k) function at separate points and symmetry lines of the Brillouin zone were derived. The calculations showed that the properties of the La_1?x Ca_xMnO₃ system do not have electron-hole symmetry.     

Optical absorption and photoconductivity of MnGaInS<Subscript>4</Subscript> single crystals in polarized light

The results of studying optical-absorption and spectral curves of photoconductivity in MnGaInS₄ single crystals are presented for two light polarizations (E || C and E ⊥ C). The intrinsic absorption edge and the band-gap width of MnGaInS4 single crystals in polarized light are determined. The anisotropy of optical absorption and photoconductivity spectrum of MnGaInS₄ single crystals is observed. It is suggested that the polarization splitting of the absorption edge is related to the splitting of the MnGaInS₄ valence band.     

Can multiband coupling effects due to remote bands cause significant normal-incidence absorption inn-type direct-gap semiconductor quantum wells?

Surprisingly, several experiments have reported that normal-incidence light absorption due to inter-conduction-subband transitions in direct-gap semiconductor quantum wells is as strong as in-plane-incidence absorption. In contrast to other models, a recent theoretical study claimed that a 14-bandk  pmodel including multiband coupling terms due toremote-conduction bandsis able to explain the experimental results. In this work, a concise formulation extends the model beyond 14 bands. Nevertheless, after rederiving the optical transition matrix elements, this analysis clearly shows that the oscillator strength for the in-plane polarized optical intersubband transition due to the multiband coupling effects is much smaller than the oscillator strength for the normal-to-plane polarized optical intersubband transition. These results indicate that the multiband coupling effects due to remote-conduction bands cannot cause a sufficient in-plane polarized optical intersubband transition to produce the observed normal-incidence absorption in the desirablen-type III–V compound semiconductor quantum wells.     

The su q(2) algebra in the off-diagonal basis and applications to quantum optics

We consider a new exactly solvable nonlinear quantum model as a Hamiltonian defined in terms of the generators of the su _q(2) algebra. The corresponding matrix elements of finite rotations (the q-deformed Wigner d functions) are introduced. It is shown that the quantum optical model of the three-wave interaction has an approximate su _q(2) dynamical symmetry given by this Hamiltonian. Such q symmetry allows us to investigate the spectral and dynamical properties of the three wave model through new perturbation techniques.     

Influence of the linear k term on the shape of the isoenergetic surfaces in p-type GaSb,deduced from galvanomagnetic measurements

From transverse or longitudinal magnetoresistance and Hall coefficient measurements performed on three samples cut in a single crystal of p-type GaSb along selected crystallographic directions, we derive six equations involving the geometric parameters of the isoenergetic surfaces. The generally admitted valence band model for GaSb is the nonquadratic model proposed by Lax and Mavroides in the case of Germanium and Silicon. We find that this model cannot account simultaneously for all the galvanomagnetic phenomena observed on p-type GaSb, in particular for the longitudinal magnetoresistance.The existence of a linear k term in the enery expression lifts the degeneracy so that the energy maxima of the valence band are not at k (000). We show then that, at 77°K, the difference between the level of the valence band maxima and the value of the energy at k (000) may be large enough to consider the existence of a multiellipsoidal structure. This structure accounts for all the observed galvanomagentic phenomena.The ellipsoids are found along (100) and (111) directions for light and heavy holes respectively. We calculate the corresponding anisotropy coefficients: K₂=1·66 and K₁=3.     

A Real Quaternion Spherical Ensemble of Random Matrices

One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the anti-sphere with truncations of unitary matrices. This paper focusses on an ensemble corresponding to the sphere: matrices of the form Y=A ^?1 B, where A and B are independent N×N matrices with iid standard Gaussian real quaternion entries. By applying techniques similar to those used for the analogous complex and real spherical ensembles, the eigenvalue joint probability density function and correlation functions are calculated. This completes the exploration of spherical matrices using the traditional Dyson indices β=1,2,4. We find that the eigenvalue density (after stereographic projection onto the sphere) has a depletion of eigenvalues along a ring corresponding to the real axis, with reflective symmetry about this ring. However, in the limit of large matrix dimension, this eigenvalue density approaches that of the corresponding complex ensemble, a density which is uniform on the sphere. This result is in keeping with the spherical law (analogous to the circular law for iid matrices), which states that for matrices having the spherical structure Y=A ^?1 B, where A and B are independent, iid matrices the (stereographically projected) eigenvalue density tends to uniformity on the sphere.