Spin-polarized electrons in atomic layer materials formed on solid surfaces

In this review, we summarize the recent progress in the understanding of the spin-polarized electronic states in two-dimensional (2D) atomic layer materials (ALMs) formed on solid surfaces. The spin-polarized electronic states caused by the combination of spin-orbit coupling (SOC) with broken spatial inversion symmetry along the surface normal direction is one of the most exotic phenomena that appears on ALMs formed on solid surfaces as well as clean solid surfaces. The so-called Rashba-Bychkov (RB) effect that arises from the potential gradient induced by broken inversion symmetry was believed to be the main origin of these spin-polarized electronic states. However, the spin texture of most ALMs are different from that caused by the ideal RB effect. Due to the high impact of the spin-polarized electronic states of 2D materials in not only spin-related fundamental science but also in applications since they are the key concepts to realize future semiconductor spintronics devices, much efforts have been made to elucidate the origin of these peculiar spin textures. So far, the deviations in spin texture from the ideal one have been attributed to be induced by perturbation, such as entanglement of spin and orbital momenta. In this review, we first illustrate how the symmetry of the ALM’s atomic structure can affect the spin texture, and then introduce that various spin textures, ranging from the RB-type and symmetry-induced type to spin textures that cannot be explained based on the origins proposed so far, can be simply induced by the orbital angular momentum. This review aims to provide an overview on the insights gained on the spin-polarized electronic states of ALMs and to point out opportunities for exploring exotic physical properties when combining spin and other physics, e.g. superconductivity, and to realize future spintronics-based quantum devices.     

Large-area periodic lead halide perovskite nanostructures for lenticular printing laser displays

Lenticular printing technique provides a promising way to realize stereoscopic displays,especially,when microscopic optical structures are integrated into light-emitting materials/devices.Here,we fabricated large-area periodic structures with a spatial resolution at a wavelength scale from hybrid perovskite materials via a space-confined solution growth method.It takes advantages of both high refractive index contrast and high luminescence brightness,which allows the optical modulation on not only the reflection of illumination,but also the light emission from hybrid perovskites.The distributed feedback within these periodic structures significantly improves the degree of polarization and directionality of laser actions while their threshold is also reduced.These findings enable us to present a prototype of lenticular printing laser displays that vary emission colors at different view angles,which may find applications in creating high-resolution and high-contrast holographical images.     

Recent progress in chiral photonic band‐gap liquid crystals for laser applications

This article describes a brief review of recent research advances in chiral liquid crystals (CLCs) for laser applications. The CLC molecules have an intrinsic capability to spontaneously organize supramolecular helical assemblages consisting of liquid crystalline layers through their helical twisting power. Such CLC supramolecular helical structures can be regarded as one‐dimensional photonic crystals (PhCs). Owing to their supramolecular helical structures, the CLCs show negative birefringence along the helical axis. Selective reflection of circularly polarized light is the most unique and important optical property in order to generate internal distributed feedback effect for optically‐excited laser emission. When a fluorescent dye is embedded in the CLC medium, optical excitation gives rise to stimulated laser emission peak(s) at the band edge(s) and/or within the CLC selective reflection. Furthermore, the optically‐excited laser emission peaks can be controlled by external stimuli through the self‐organization of CLC molecules. This review introduces the research background of CLCs carried out on the PhC realm, and highlights intriguing precedents of various CLC materials for laser applications. It would be greatly advantageous to fabricate active CLC laser devices by controlling the supramolecular helical structures. Taking account of the peculiar features, we can envisage that a wide variety of supramolecular helical structures of CLC materials will play leading roles in next‐generation optoelectronic molecular devices. © 2010 The Japan Chemical Journal Forum and Wiley Periodicals, Inc. Published online in Wiley InterScience ( www.interscience.wiley.com ) DOI 10.1002/tcr.201000013     

Symmetrization of eigenfunctions of angular momentum in point groups

The eigenfunctions |jm〉 of angular momentum can combine linearly to make basis functions of irreducible representations of point groups. We surmount the projection operator and find a new method to calculate the combination coefficients. It is proven that these coefficients are components of eigenvectors of some hermitian matrices, and that for all pure rotation point groups, the coefficients can be made real numbers by properly choosing the azimuth angles of symmetry elements of point groups in the coordinate system. We apply the coupling theory of angular momentum to obtain the general formulas of the basis functions of point groups. By use of our formulas, we have calculated the basis functions with half‐integers j from 1/2 to 13/2 of double‐valued irreducible representations for the icosahedral group. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 286–302, 2001     

Basics of optical force

Light possesses momentum, and hence, force is exerted on materials if they absorb and/or scatter light. Laser techniques that use optical forces are currently attracting considerable attention. Optical manipulation for trapping, transporting small particles, and measuring the interparticle force is a representative technique. In addition, photoinduced force microscopy is a promising scanning type of microscopy using optical force. Optical force techniques have recently been used in various fields of research, such as molecular bioscience, organic photochemistry, materials engineering, and molecular fluid dynamics. In these techniques, several types of optical forces such as scattering, absorption, and gradient forces play their respective roles. In this article, we summarize the basics of optical forces and present their elementary expressions for using simplified models of light and matter systems. This will help the readers of this Special Issue to understand how different types of forces are distinguished in the basic expressions used for analyzing the optical force phenomena that appear depending on the light geometry and matter systems. After observing simplified cases of scattering and absorption forces, we introduce general formulae for the optical force and then discuss how different components appear in particular cases of laser geometry and materials.     

Entanglement of angular momenta of atoms and molecules

In this article, we investigate the entanglement degrees of angular momenta of atoms and molecules. We demonstrate theoretically and numerically the guidelines, how to prepare maximally entangled states and how the entanglement of the angular momenta changes by changing the quantum numbers of atoms and molecules. We show that the entanglement degree reduces to the Clebsch–Gordan coefficients frequently encountered in angular momentum theory. The maximally entangled states found in this manner are useful for quantum computers and quantum information science. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Spin,orbit, and parity conservation in rotation changing collisions

Three series of paradoxical experiments on diatom-atom rotational energy transfer (RET) are reviewed. Resolution of the paradoxes leads to two propensity rules governing parity changes in RET collisions: (i) electronic spin orientation is conserved; and (ii) orbital angular momentum orientation is preserved in polar molecule-atom RET.     

Current-induced rotation of helical molecular wires

We show that electric current running through a nanojunction with a biased helical molecule can induce unidirectional rotation of the molecular component. In an electric field, conduction electrons injected into the molecule are accelerated along the helical path going through its body, thereby gaining directed angular momentum. Conservation laws require that an angular momentum of the same size but opposite sense is imparted to the rigid-body rotation of the helix. We describe the angular momentum exchange processes that underlie the operation of the nanorotor, discuss factors limiting its efficiency, and propose potential applications.     

An animated visualization of orbital angular momentum and spin‐orbit coupling

This paper presents an approach toward visualizing a complex orbital based on animation using a time‐dependent phase factor. This makes orbital angular momentum clearly visible, in a way that reflects the nature of the orbital angular momentum wavefunction. Visualization of this quantity is also useful for examining the effects of spin‐orbit coupling (SOC), in which higher orbital angular momentum states are admixed into the orbital; in this case, however, scaling of one phase‐component is needed. The phase orientation of a complex orbital, which is generally not guaranteed by the SCF procedure, must be considered when doing this. The method of visualization presented here may prove useful when analyzing properties where SOC is important, such as magnetic resonance parameters. Animated visualizations are performed, and compared with the method of phase‐colored isosurfaces, first for a model p‐orbital to explain the idea, and then for the singly‐occupied molecular orbitals of two small doublet radicals.     

Polarized laser-induced photofragmentation studies of JKM-selected CH3I molecules: retention of orientation in optical and DC electric fields

The technique of linearly polarized laser-induced photofragmentation for the measurement of the degree of orientation of rotationally state-selected symmetric top molecules [Phys. Rev. Lett.59, 2951 (1987)] has been used to study the retention of molecular orientation in optical frequency AC and homogeneous DC electric fields. For CH₃I beams, state-selected by the electrostatic hexapole focuser in several specific low-J parent states, recoupling of the iodine nuclear spin with the molecular rotational angular momentum occurs rapidly in weak fields, leading to some loss of orientation, but the resulting degree of orientation (i.e., theM _F distribution) is retained in both DC and optical frequency electric fields. The direction of the orientation of the molecular axis can be inverted with 100% efficiency by changing the sign of the DC ‘orienting field’. The up/down asymmetry of the photofragment angular distribution can be observed with either parallel (vertical) or perpendicular (horizontal) laser polarization.     

Local angular momentum as ring strain descriptor

A new method is demonstrated to quantify local ring strain, which is based on the expectation value of orbital angular momentum along the internuclear axis. In contrast to energy based methods which provide overall ring strain, this method is able to identify the local strain in every part of the ring. The formalism is benchmarked on several cycloalkanes in which the presence of ring strain is well understood. The ring strain plays a decisive role in carbon nanotubes (CNTs) properties; for instance, the hydrogen storage capability of CNTs is related to their diameter, which in turn has a close relation to the ring strain in their C? C bonds. On this basis, the ring strain in five CNTs with different diameters is analyzed and the results reflected meaningful correlation between the CNTs diameter and ring strain. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Present status of the functional advanced micro-, nano-printings – a mini review

Additive printing technology and expertise have experienced noteworthy development driven by their ability to revolutionize academic and industrial manufacturing and research. They also have particular practical uses in the areas of micro and nanofabrication. Micro- and nano-printings have found a tremendous number of applications in material synthesis/patterning, electronics, medicine and biotechnology. In this mini review, we examine the important additive micro and nano printing techniques, including contact and noncontact, and roll to roll (R2R) printing methods as well as recently emerging techniques such as micro- or nano-pen printings, laser-induced forward transfer (LIFT) and aerosol jet printing (APJ). We also discuss the materials that are printable by these technologies, the applications of micro- and nano-printings, key features, advantages and challenges.     

Anisotropy in the interaction of ultracold dysprosium

The nature of the interaction between ultracold atoms with a large orbital and spin angular momentum has attracted considerable attention. It was suggested that such interactions can lead to the realization of exotic states of highly correlated matter. Here, we report on a theoretical study of the competing anisotropic dispersion, magnetic dipole-dipole, and electric quadrupole-quadrupole forces between two dysprosium atoms. Each dysprosium atom has an orbital angular momentum of L = 6 and a magnetic moment of μ = 10 μ(B). We show that the dispersion coefficients of the ground state adiabatic potentials lie between 1865 a.u. and 1890 a.u., creating a non-negligible anisotropy with a spread of 25 a.u. and that the electric quadrupole-quadrupole interaction is weak compared to the other interactions. We also find that for interatomic separations R < 50a(0) both the anisotropic dispersion and magnetic dipole-dipole potential are larger than the atomic Zeeman splittings for external magnetic fields of order 10 G to 100 G. At these separations the atomic angular momentum can be reoriented. We finish by describing two scattering models for these inelastic m-changing collisions. A universal scattering theory is used to model loss due to the anisotropy in the dispersion and a Born approximation is used to model losses from the magnetic dipole-dipole interaction for the (164)Dy isotope. These models find loss rates that are of the same order of magnitude as the experimental value.     

Frequency modulated spectroscopy as a probe of molecular collision dynamics

We describe the application of frequency modulated spectroscopy (FMS) with an external cavity tuneable diode laser to the study of the scalar and vector properties of inelastic collisions. CN X(2)Sigma(+) radicals are produced by polarized photodissociation of ICN at 266 nm, with a sharp velocity and rotational angular momentum distribution. The collisional evolution of the distribution is observed via sub-Doppler FMS on the A(2)Pi-X(2)Sigma(+) (2,0) band. He, Ar, N(2), O(2) and CO(2) were studied as collider gases. Doppler profiles were acquired in different experimental geometries of photolysis and probe laser propagation and polarization, and on different spectroscopic branches. These were combined to give composite Doppler profiles from which the speed distributions and specific speed-dependent vector correlations could be determined. The angular scattering dynamics with species other than He are found to be very similar, dominated by backward scattering which accompanies transfer of energy between rotation and translation. The kinematics of collisions with He are not conducive to the determination of differential scattering and angular momentum polarization correlations. Angular momentum correlations show interesting differences between reactive and non-reactive colliders. We propose that this reflects differences in the potential energy surfaces, in particular, the nature and depth of attractive potential wells.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

Local physical quantities for spin based on the relativistic quantum field theory in molecular systems

Local physical quantities for spin are investigated on the basis of the four‐ and two‐component relativistic quantum theory. In the quantum field theory, local physical quantities for spin such as the spin angular momentum density, spin torque density, zeta force density, and zeta potential play important roles in spin dynamics. We discuss how to calculate these local physical quantities based on the two‐component relativistic quantum theory. Some different types of relativistic numerical calculations of local physical quantities in Li atom and C₆H₆ are demonstrated and compared. Local physical quantities for each orbital are also discussed, and it is seen that a total local zeta potential is given as a result of some cancellation of large contributions from each orbital. © 2016 Wiley Periodicals, Inc.     

An optically driven pump for microfluidics

We demonstrate a method for generating flow within a microfluidic channel using an optically driven pump. The pump consists of two counter rotating birefringent vaterite particles trapped within a microfluidic channel and driven using optical tweezers. The transfer of spin angular momentum from a circularly polarised laser beam rotates the particles at up to 10 Hz. We show that the pump is able to displace fluid in microchannels, with flow rates of up to 200 microm(3) s(-1) (200 fL s(-1)). The direction of fluid pumping can be reversed by altering the sense of the rotation of the vaterite beads. We also incorporate a novel optical sensing method, based upon an additional probe particle, trapped within separate optical tweezers, enabling us to map the magnitude and direction of fluid flow within the channel. The techniques described in the paper have potential to be extended to drive an integrated lab-on-chip device, where pumping, flow measurement and optical sensing could all be achieved by structuring a single laser beam.     

角动量耦合与原子光谱项

介绍了量子力学中两个角动量耦合的通用方法,并从角动量守恒的观点分析了原子光谱项的推导基础。     

Light-controlled movement of isotropic droplets in smectic films

This paper reports on optical trapping of micrometre-sized isotropic inclusions in free-standing smectic A* films. Droplet manipulation and trapping potential in such a two-dimensional anisotropic system show that optical trapping has two distinct regimes with unique separation dependence, governed by long-range and short-range trapping forces and enhanced diffusivity at the free surfaces. Molecular ordering in the surface layers of isotropic inclusions, at the liquid crystal–air interface, in addition leads to a new field of light-controlled particle dynamics. For low laser powers, translational motion of a droplet along the laser polarisation is observed. Above the threshold laser power, the transfer of optical angular momentum to the inclusion via linearly polarised light leads to circular-like motion. As the optical torque for a given intensity is counterbalanced by the elastic torque of the smectic film, this motion results in finite angle steps.     

The primitive L-pattern of angular momentum recoupling coefficients

Labarthes primitive L-patterns for the 3nj-symbols, where n=3,4,5,6,7, are reported. It is shown that, any L-patterns of the angular momentum recoupling coefficients can be expressed in terms of linear combinations of the primitive L-patterns and how the 3nj-symbols can be calculated from the expressions presented here.AMS subject classification: 81QShan-Tao Lai–Permanent Address for reprint requestYing-Nan ChiuAlso– Institute of Atomic and Molecular Sciences, Academia Sinica,Taipei, Taiwan, R.O.C.