Lack Of Inversion Symmetry Research Articles

Vortex states in antiferromagnetic crystals

It is shown that axially symmetric two-dimensional nonuniform states can exist in easy-axis and cubic antiferromagnets lacking inversion symmetry, in the form of two-dimensional spatially modulated structures (magnetic vortex lattices) and isolated two-dimensional structures (vortices). The structure and equilibrium dimensions of the lattices and vortices have been determined by numerical solution of differential equations.

Efficiency of optical second harmonic generation from pentacene films of different morphology and structure

Submicron thick polycrystalline pentacene films of different morphology and molecular configuration are prepared by varying the conditions during vacuum deposition on quartz, sapphire and Si substrates. The films are characterized by X-ray diffraction, atomic force microscopy, optical absorption, and Raman spectroscopy. The efficiency of optical second harmonic generation (SHG) is studied as a function of the film properties using picosecond laser pulses at a fundamental wavelength of 1064 nm and femtosecond pulses at a fundamental wavelength of 870 nm. The second-order nonlinearity originates from the lack of inversion symmetry at the surfaces of the crystallites and is practically independent of the structure and morphology of the films. An abnormally low efficiency of SHG from films deposited at room temperature is explained by scattering of the second harmonic at crystals of a size comparable to the wavelength of the second harmonic.

Parametric Study of Reflection Characteristics at Ahiral-Chiral Interfaces

Materials described by the constitutive relations σji=µγji+µγij+λγkkδij+cκji and χji=(ξ+ε)κji+(ξ-ε)κij+ηκkkδij+cγji lack inversion symmetry due to chirality in their microstructures. Six wavenumbers are possible solutions for dispersion equations in acoustically active (chiral) medium. Two of these wavenumbers represent longitudinally polarized elastic waves, the remaining four wavenumbers stand for circularly polarized elastic waves. In this paper, reflection characteristics of elastic waves normally impinging upon achiral-chiral interfaces are thoroughly discussed. The effects of the constitutive parameters of chiral medium on reflection coefficients are elucidated. Simulation results illustrate that reflection coefficients may vanish by properly tailoring constitutive parameters of chiral medium. The methods for determining constitutive parameters of chiral medium for zero reflection at achiral-chiral interfaces are developed. Results obtained in this study can be applied for designing state-of-the-art acoustic materials, e.g. acoustic shielding and absorptive materials, using chiral composites.

Spin splittings in nanostructures without inversion symmetry

Abstract

Evaluation of matrix elements of the 8 x 8 k

The k\ensuremath{\cdot}p method of band-structure calculation provides a detailed description of a crystal's energy dispersion near a high symmetry point in the first Brillouin zone. The resulting parameters of this calculation are a series of momentum matrix elements. Presented here is a set of band-structure parameters for the zinc-blende structure of GaAs at the \ensuremath{\Gamma} point that takes the lack of inversion symmetry into account as well as k-dependent spin-orbit contributions to the Hamiltonian. A comprehensive optimization was performed in order to satisfy effective mass data as well as conduction band spin-splitting data. It was found that the lack of inversion symmetry has a profound influence on the nonparabolicity of the conduction band and the contribution of the k-dependent spin-orbit effect cannot be ignored in the calculation of the effective mass of the conduction, light hole, and spin-orbit bands. \textcopyright{} 1996 The American Physical Society.

Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy.

High momentum resolution angle resolved photoemission spectra from the Au(111) $\mathrm{sp}$-derived surface state exhibit a doublet. The separation between the peaks increases linearly with ${k}_{\ensuremath{\Vert}}$, and reaches a maximum of 110 meV at $0.153{\AA{}}^{\ensuremath{-}1}$, when one of the bands crosses the Fermi level. These results are interpreted as spin-split surface state bands, with the spins aligned in the plane of the surface perpendicular to the electronic momentum. The origin of the splitting is spin-orbit coupling, which can break spin degeneracy in systems which lack inversion symmetry.

Competition between spin, charge, and bond waves in a Peierls-Hubbard model.

We study a one-dimensional extended Peierls-Hubbard model coupled to intracell and intercell phonons for a half-filled band. The calculations are made using the Hartree-Fock and adiabatic approximations for arbitrary temperature. In addition to static spin, charge, and bond density waves, we predict intermediate phases that lack inversion symmetry, and phase transitions that {ital reduce} {ital symmetry} {ital on} {ital increasing} {ital temperature}. {copyright} {ital 1996 The American Physical Society.}

Weak anti-localisation in 2-D 100-electron gases in GaAS

2-dimensional electrons in GaAs has a strong spin-orbit interaction, which leads to anti-localisation. The origin of this spin-orbit effect in GaAs lies in the band structure, where an intrinsic spin splitting is rooted in the lack of inversion symmetry. The weak localization at small magnetic fields clearly shows this. We have studied this experimentally at various temperatures in 2 different MBE grown GaAlAs/GaAs structures: A triangular 100 oriented quantum well and a symmetrical 100 oriented quantum well.

Generalized superlattice K

The eight-band superlattice crystal K\ifmmode\cdot\else\textperiodcentered\fi{}p formalism is extended to include the higher-lying antibonding $p$ states perturbatively. The initial 14\ifmmode\times\else\texttimes\fi{}14 Hamiltonian matrix is block diagonalized (or folded down) so that corrections due to these states appear in the modified 8\ifmmode\times\else\texttimes\fi{}8 matrix. Their principal effect is to introduce a finite heavy-hole mass. The use of the eight-band formalism for band-structure and interband optical calculations is validated because other corrections are very small. The approximate wave functions associated with the original 14\ifmmode\times\else\texttimes\fi{}14 Hamiltonian are used to calculate intersubband optical matrix elements. These include new terms, present in crystals lacking inversion symmetry, which increase the magnitude of conduction intersubband absorption by about three orders of magnitude for in-plane polarized (TE) photons, while leaving absorption due to growth-axis polarized (TM) photons relatively unaffected. The TE absorption in narrow $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wells (QW's) is shown to be observable. However, use of the $f$-sum rule and the cyclotron-resonance-determined conduction-band effective-mass anisotropy indicate an upper limit of about 20% relative to TM absorption. Comparison with the measured TM absolute absorption coefficient for a system used for quantum-well infrared photoconductors (QWIP's) yields excellent agreement. The conductivity sum rule involving these intersubband transitions is used to confirm the observed broadening associated with very small QW width fluctuations for this system.

Electron-gas clusters: the ultimate jellium model

The local spin-density approximation is used to calculate ground- and isomeric-state geometries of jellium clusters with 2 to 22 electrons. The positive background charge of the model is completely deformable, both in shape and in density. The model has no input parameters. The resulting shapes of the clusters exhibit breaking of axial and inversion symmetries; in general the shapes are far from ellipsoidal. Those clusters which lack inversion symmetry are extremely soft against odd-multipole deformations. Some clusters can be interpreted as molecules built from magic clusters. The deformation produces a gap at the Fermi level. This results in a regular odd-even staggering of the total energy per electron and of the HOMO level. The strongly deformed 14-electron cluster is semimagic. Stable isomers are predicted. The splitting of the plasmon resonance due to deformation is estimated on a classical argument.

Stimulated Brillouin scattering in magnetized direct-gap semiconductors.

Following the time-dependent perturbation technique for the density matrix, the phenomenon of stimulated Brillouin scattering (SBS) has been analytically studied in weakly noncentrosymmetric (NCS) crystals like InSb immersed in a moderately strong magnetostatic field. The twofold role of the magnetostatic field B in terms of the sharpening of the density of states and Landau-level splitting have been examined quantum mechanically. The extremely large value of the spectroscopic splitting factor (${\mathit{g}}_{\mathit{c}}$-${\mathit{g}}_{\mathit{v}}$) and the very low electron and hole effective masses play the key roles in the significant enhancement in Brillouin susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathbf{B}}$, even when B is reasonably low. The origin of the NCS effect has been assumed to be in the parity indefiniteness of the energy states in the crystals exhibiting lack of inversion symmetry. We have considered near-resonant band-to-band electron transition in the direct-gap crystals to reduce to a simple one-dimensional problem in the presence of the magnetostatic field. Numerical estimates have been made for the InSb crystal at 77 K, duly irradiated by a pulsed 5.3 \ensuremath{\mu}m CO laser. The SBS threshold is found to be well below the crystal damage threshold and ${\mathrm{\ensuremath{\chi}}}_{\mathbf{B}}$ is found to be appreciably large. The results support strongly the candidacy of InSb for establishing itself as a promising crystal for strong SBS and optical-phase conjugation while immersed in a moderate magnetostatic field.

Measurement of the electromagnetic properties of chiral composite materials in the 8–40 GHz range

Materials described by the constitutive equations D = εE + βε ∇ × E and B = μH + βμ ∇ × H lack inversion symmetry due to chirality or handedness in their microstructure. In this paper, we describe the first direct measurements of the material properties ε, μ, and β for microwave chiral composite materials prepared in our laboratory in the frequency range of 8–40 GHz. We have used both reflection and transmission measurements for normally incident, linearly polarized plane waves in a specially designed free‐space facility using spot focusing antennas. Different concentrations of the chiral inclusions in the form of miniature metallic springs that are left‐handed only, right‐handed only or equally mixed (racemic) have been studied. It is shown that ε and μ are comparable for all three samples at a given concentration, but β has equal but opposite values for the left‐ and right‐handed samples, whereas it is nearly zero for the equichiral sample. The values of β thus obtained are compared to estimated values for suspensions of naturally occurring chiral molecules. The accuracy of the measurements is assessed by using the experimental procedure and inversion algorithm for standard materials like quartz. A new technique involving time domain repines has been used to remove the ambiguity that is usually encountered in the inversion of measured S parameters.

Second-harmonic generation in thin films of copper phthalocyanine.

We have observed the optical second-harmonic generation (SHG) from a polycrystalline film of copper phthalocyanine (CuPc) with thicknesses between 40 and 2000 K. The nonlinear susceptibility of this film is χ ZYY (2) =1.89×(3/4π)×10 -7 esu where Z and Y are the directions perpendicular and parallel to the film surface, respectively. This value is unexpectedly large, approaching a quarter of the value for the well-known nonlinear optical crystal LiNbO 3 . The finite value of the nonlinear susceptibility indicates that the structure of this film lacks inversion symmetry. The polarisation properties of the second-harmonic (SH) light show that the film lacks inversion symmetry perpendicular to the film surface

Determination of ratios between nonlinear-optical coefficients by using subpicosecond optical rectification

We present a qualitative description of subpicosecond optical rectification and a detailed description of its application in, determining the ratios between nonlinear-optical coefficients. We propose the experimental determination of ratios between second-order optical rectification coefficients in all 15 point groups lacking inversion symmetry and having two or more independent nonvanishing nonlinear-optical coefficients in seven crystal structures. We have chosen three common nonlinear-optical crystal structures, cubic, trigonal, and monoclinic, in our experiments. The experimental results on GaAs, LiTaO3, and organic crystals agree with our theoretical calculation and previously reported data and demonstrate the potentiality and feasibility of the novel technique. We believe that this technique will play an important role in the characterization and development of novel nonlinear-optical materials.

Intrasubband excitations and spin-splitting anisotropy in GaAs modulation-doped quantum wells.

We present Raman-scattering measurements of intrasubband excitations in the quasi-two-dimensional electron gas (2DEG) of an n-type modulation-doped GaAs/${\mathrm{Al}}_{0.33}$${\mathrm{Ga}}_{0.67}$As quantum well. In depolarized spectra we observe spin-flip single-particle excitations between the spin-split conduction bands. Measurements with the Raman wave vector along different crystallographic orientations allow us to probe the anisotropy of this spin splitting, caused by the lack of inversion symmetry in GaAs. We discuss theoretical descriptions of the spin splitting in a 2DEG and compare calculated and measured Raman spectra. In polarized spectra we observe scattering with comparable intensity from non-spin-flip single-particle excitations and plasmons. In order to describe correctly the plasmon dispersion we have to take into account the effects on the Coulomb interaction of image charges in the sample surface.

Conduction-subband anisotropic spin splitting in III-V semiconductor heterojunctions.

The electrostatic potential experienced by a conduction electron at a III-V semiconductor heterojunction is a sum of the macroscopic confining and the microscopic bulk potentials. Both of them lack inversion symmetry. Two origins for the spin-orbit spin splitting can be assigned. We point out that, in first order in the in-plane wave vector ${\mathit{k}}_{\mathrm{\ensuremath{\parallel}}}$, the ${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$-dependent total spin splitting is highly anisotropic. The anisotropy increases as the ratio of the two contributions approaches unit and results from their interference. The relative size of the two spin splitting mechanisms, as a function of the electric field at the interface, is estimated for heterojunctions based on different III-V semiconductor compounds. Observable effects of the anisotropy in the spin splitting are predicted.

Origin of the forbidden transitions in diluted magnetic semiconductors

Mechanisms for the intraionic optical transitions in Mn-based diluted magnetic semiconductors are analyzed on the basis of two possible models. A simple model for these transitions based on a proposal by Lacueva and Overhauser does not seem to be tenable. We conclude that the transition 6S → 4G observed in Cd 1− x Mn x Te and Zn 1− x Mn x Te is due to electric-dipole interactions made possible by the lack of inversion symmetry and the presence of the spin-orbit interaction.

Angular dependence of optical second-harmonic generation at a Ge(111) surface

The variation of the second-harmonic signal with the incident angle is studied for both isotropic and anisotropic contributions, which arise from a lack of inversion symmetry along the surface normal and in the surface plane, respectively. For Ge(111) the angular dependence of the different contributions is in good agreement with theoretical predictions. The results show that accurate determination of surface and bulk contributions from angular-dependence data is difficult for materials with high dielectric constants, such as Ge. From a comparison of intensity ratios of (111) and (001) crystal faces, we determined that surface and bulk terms make comparable contributions to the second-harmonic signal of Ge(111) at the chosen excitation wavelength.

Spectroscopy studies of lanthanide trichloroacetate single crystals

The single crystals of some lanthanide carboxylates are characterized by a lack of inversion symmetry, so they could be used for generation of the second harmonic. 1−5 Single crystals of neodymium and erbium trichloroacetate were synthesized and shown to form the polymeric chain linking dimeric subunits, where the lanthanide ions can occupy different site symmetry positions. The absorption and luminescence spectra of single crystals of the title compounds were measured at room and liquid helium temperatures; Stark components were determined and analysed in terms of interacting ions. Spectroscopic properties were related to the X-ray crystal data. Probabilities of f- f transitions depending on the orientation of biaxial single crystals were considered.

Effect of magnetostatic field on the second-order optical susceptibility of III-V semiconductors

An analytical investigation of the application of a large magnetostatic field on the second-order optical susceptibility χ(2) in III-V semiconductors like GaAs and InSb is reported. The model is based upon the parity indefiniteness of the electron wave functions in crystals lacking inversion symmetry. The generalized force and the electronic dipole moment operators are accordingly taken to be 2×2 matrices with all elements being finite. We have followed perturbation technique for the density matrix. The magnetostatic field renormalizes the transition frequency and sharpens the density of states. Both the resonant as well as nonresonant three-wave parametric interactions have been discussed. Numerical estimates made for InSb crystal under resonant regime reveal considerable enhancement in the real part of χ(2) even at moderately low magnetic field while the imaginary part exhibits a near saturation behavior. Under nonresonant laser excitation, both χ(2)r and χ(2)i rise very sharply with magnetic field for effective cyclotron frequency ωc≤ω0−ωg, ω0 and ωg being the pump and crystal band-gap frequencies, respectively. Quite interestingly, χ(2)r and χ(2)i decay almost exponentially to very low values at ωc>2(ω0−ωg).