Conductance of a large point contact with Rashba effect

We study the scattering of an electron of a 2DEG through a large point contact separating a region where the electrons are free and a region where the Rashba spin-orbit coupling is present. The scattering depends dramatically on the electron incidence angle showing double refraction within the Rashba region. For incidence not normal to the interface the electron spin state is not conserved. The calculated conductance exhibits an oscillating behavior as a function of spin state of the incident electrons with different spin down and spin up currents. Our model describes both a ferromagnetic semimetallic source and a simple metallic injection electrode. In the first case the electrons are injected in a pure spin state and in the second one they are unpolarized, that is in a statistical mixture of spin up and down states. In both the cases the passage through the large point contact produces spin polarized currents.Received: 30 July 2003, Published online: 23 December 2003PACS: 85.75.Hh Spin polarized field effect transistors - 72.25.-b Spin polarized transport - 73.23.Ad Ballistic transport     

The reflectivity of relativistic ultra-thin electron layers

The coherent reflectivity of a dense, relativistic, ultra-thin electron layer is derived analytically for an obliquely incident probe beam. Results are obtained by two-fold Lorentz transformation. For the analytical treatment, a plane uniform electron layer is considered. All electrons move with uniform velocity under an angle to the normal direction of the plane; such electron motion corresponds to laser acceleration by direct action of the laser fields, as it is described in a companion paper [Eur. Phys. J. D 55, 433 (2009)]. Electron density is chosen high enough to ensure that many electrons reside in a volume λ_R ³, where λ_R is the wavelength of the reflected light in the rest frame of the layer. Under these conditions, the probe light is back-scattered coherently and is directed close to the layer normal rather than the direction of electron velocity. An important consequence is that the Doppler shift is governed by γ_x=(1-(V_x/c)²)^-1/2 derived from the electron velocity component V_x in normal direction rather than the full γ-factor of the layer electrons.     

Spin Polarization Oscillation and Spin-Polarized Diode Based on Graphene Rashba–Strain Double Junctions

We investigate spin-dependent electron transport through graphene-based Rash ba-strain double junctions. It is found that when electrons are injected from left normal graphene region, high spin polarization oscillation is achieved due to the wave-vector-dependent resonant tunneling. The spin polarization is negligible once the incident direction is reversed. Such a remarkable difference arises from pseudogap caused by the Rashba spin-orbit interaction.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

The Discrete Spectrum in the Gaps of the Continuous One for Non-Signdefinite Perturbations with a Large Coupling Constant

Given two selfadjoint operators A and V=V ₊ -V _-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N ₊(λ,α), N _-(λ,α), N ₀(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger operators and its generalizations are given. Received: 9 April 1997 / Accepted: 26 August 1997     

Photocontrolled magnetic resonance plasticity of γ-irradiated KCl:Fe crystals

A photocontrolled resonance decrease in microhardness, which is due to the application of mutually perpendicular static and microwave fields, in γ-irradiated KCl:Fe crystals has been revealed. It has been found that the magnetic plasticity of unirradiated γ-KCl:Fe crystals is due to the resonance effect of magnetic fields on two types of impurity centers: first, centers containing Fe²⁺-ν _c ion-vacancy pairs and, second, centers containing Fe⁺ ions. The illumination of γ-KCl:Fe crystals with F-light (with a wavelength of λ = 500–600 nm) is accompanied by rearrangement of the spectrum of electron paramagnetic resonance detected by a change in microhardness. The effect of F-light on the spectrum of magnetic resonance plasticity is manifested as the suppression of the spectra of Fe²⁺-ν _c ions with effective g-factors of 7.0 and 3.5 due to their recombination with F-electrons and reconstruction to Fe⁺ centers with g-factors of 2.2 and 4.1.     

The dynamical mixing of light and pseudoscalar fields

We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions L _int = g _ϕ ϕε _μναβ F ^μν F ^αβ . The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.      

Ground state structure of some double-λ hypernuclei by a three-body model using a simple coordinate space approach

New experimental data on the binding energyB _λλ of_λλ6He, reported very recently, come up with the valuesB _λλ = 725 ±0.14 MeV and ΔB_λλ = 101 ±0.2 MeV which are substantially lower than the old dataB _λλ = 109 ±0.8 MeV and ΔB_λλ = 4.7±10 MeV in use in literature since 1966. In view of the new data we decided to undertake a re-study of the _λλ ⁶ He hypernucleus using the same three-body model (α-λ-λ) with a simple coordinate space variational approach which was employed earlier with the old data on_λλ/6He. After fitting different λ-λ potentials to the new data of _λλ ⁶ He we have applied our method to study some double-λ hypernuclei in light, medium and heavy mass regions and have determined the structural quantities like Bλλ, the r.m.s. values of core-λ (〈r_core-λ〉〉) and λ-λ (〈r_λ-λ〉〉) distances theoretically. The core-λ interaction considered is of Woods-Saxon type. The strength and the range of the core-A potential have been adjusted to reproduce the λ-binding energy(B _λ) . These are in good agreement with the relativistic mean field (RMF) results. Our study shows that the λ-λ bonding energy ΔB_λλ decreases with increasing mass number from _λλ ¹⁰ Be to _λλ ²¹⁰ Pb of a double-A hypernucleus     

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

Wave packet splitting and zitterbewegung in two-dimensional semiconductor structures with spin-orbit coupling

Dynamics of electron wave packets in an asymmetric quantum well in the presence of Rashba spinorbit coupling was analytically and numerically studied. Electron Green’s functions were introduced and the evolution of 1D and 2D wave packets was studied. The effect of packet splitting caused by the presence of two branches with different chiralities in the Rashba Hamiltonian spectrum and zitterbewegung, i.e., packet center’s jitter, was studied. Spatial components of the spin density were calculated. It was shown that the component of the spin density S _y in split parts of the wave packet has opposite signs, and two other spin density components oscillate in space between scattering packets.     

The Parameter Planes of λz<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript> exp(z) for <Emphasis Type="Italic">m</Emphasis> ≥ 2*

We consider the families of entire transcendental maps given by F _λ,m (z) = λz ^m exp(z), where m ≥ 2. All functions F _λ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A ^*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A ^*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of which serve as a model for F _λ,m , in the sense that they are related by means of quasiconformal surgery to F _λ,m . Both authors were supported by MTM2005-02139/Consolider (including a FEDER contribution) and CIRIT 2005 SGR01028. The first author was also supported by MTM2006-05849/Consolider (including a FEDER contribution).     

On Minimal Eigenvalues¶of Schrödinger Operators on Manifolds

We consider the problem of minimizing the eigenvalues of the Schr?dinger operator H=−Δ+αF(κ) (α>0) on a compact n-manifold subject to the restriction that κ has a given fixed average κ₀. In the one-dimensional case our results imply in particular that for F(κ)=κ² the constant potential fails to minimize the principal eigenvalue for α>α_c=μ₁/(4κ₀ ²), where μ₁ is the first nonzero eigenvalue of −Δ. This complements a result by Exner, Harrell and Loss, showing that the critical value where the constant potential stops being a minimizer for a class of Schr?dinger operators penalized by curvature is given by α _c . Furthermore, we show that the value of μ₁/4 remains the infimum for all α >α _c . Using these results, we obtain a sharp lower bound for the principal eigenvalue for a general potential. In higher dimensions we prove a (weak) local version of these results for a general class of potentials F(κ), and then show that globally the infimum for the first and also for higher eigenvalues is actually given by the corresponding eigenvalues of the Laplace–Beltrami operator and is never attained. Received: 17 July 2000 / Accepted: 11 October 2000     

Analysis of THz-wave surface-emitted difference-frequency generation in periodically poled lithium niobate waveguide

It was shown that the periodically poled LiNbO₃-waveguide with period of poling λ≈λ/n_g (λ is the wavelength of emitted THz-wave, n_g is a refractive index corresponding to optical group velocity) emits THz-wave difference-frequency generation (DFG) in the direction normal to the surface of the planar waveguide. The 5% distinction between the manufactured and required periods of gratings results only in a small deflection (∼6°) of the output THz-beam from the normal direction. The dependence of DFG efficiency on mode size is analyzed. The output THz power at λ=150 μm is estimated as 2 mW, taking into account imperfections in coupling incident beams with guided modes. It was shown that the efficiency of THz-wave DFG in surface-emitting geometry is more than for collinear geometry in bulk crystal, especially in the high-absorption wavelength region. Received: 16 May 2001 / Revised version: 13 August 2001 / Published online: 2 November 2001     

A μSR Study of Er Spin Dynamics in (Y1−x Er x )Ni2B2C Superconductors

Zero field μSR has been used to probe rare earth spin dynamics in the magnetic superconductors, Y_1−x Er _x Ni₂B₂C. The muon spin relaxation function is stretched exponential, exp (−(λt)^β), in form, as usually found for spin glass systems above the glass temperature. However, the Y_1−x Er _x Ni₂B₂C compounds show no evidence of coexisting superconducting and static spin glass ground states even at concentrations below the critical value (x=0.6) for long range antiferromagnetic order. The temperature dependence of both the muon spin relaxation rate λ and the exponent β suggests that Er spin dynamics change significantly at the superconducting transition temperature. This revised version was published online in September 2006 with corrections to the Cover Date.     

Refraction of <Emphasis Type="Italic">s</Emphasis>- and <Emphasis Type="Italic">p</Emphasis>-polarized electromagnetic waves at the interface between a nonmagnetic insulator and an easy-axis centroantisymmetric antiferromagnet

Using the example of an easy-axis antiferromagnet with a magnetic structure of 4 _z ⁻2 _x ⁺ I ⁻ the effect of antisymmetric magnetoelectric interaction on the nature of the refraction of the bulk s- or p-polarized electromagnetic waves, incident from outside at any angle to the surface of the magnet, is studied analytically. The easy magnetic axis is collinear to the normal to the medium interface.     

The exponent λ (x, Q2) of the proton structure functionF2(x, Q2) at lowx

The exponent λ of the structure function F₂ ∼x ^−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ ² and as a function ofQ ² at fixedx and compared with the most recent data from H1     

Study of opto-mechanical characteristics of interaction of ultrashort laser pulses with polymer materials

The opto-mechanical characteristics, such as the specific mechanical recoil momentum, the specific impulse, and the energy efficiency, of the laser ablation of flat polymer targets ((C₂F₄) _n , (CH₂O) _n ) have been determined experimentally for the first time for the case of excitation with femtosecond pulses (τ ∼ 45–70 fs) of UV-IR (λ ∼ 266, 400, 800 nm) laser radiation (I ₀ up to 10¹⁵ W/cm²) under normal atmospheric and vacuum (p ∼ 10⁻⁴ mbar) conditions. The efficiency of mechanical recoil momentum generation is analyzed for various regimes of the laser irradiation.     

Gauge Theoretical Equivariant Gromov–Witten Invariants and the Full Seiberg–Witten Invariants¶of Ruled Surfaces

Let F be a differentiable manifold endowed with an almost K?hler structure (J,ω), α a J-holomorphic action of a compact Lie group on F, and K a closed normal subgroup of which leaves ω invariant. The purpose of this article is to introduce gauge theoretical invariants for such triples (F,α,K). The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface Σ. Our main results concern the special case of the triple