Velocity fluctuations of a column of water streaming down a wire: the possibility of one-dimensional turbulence

In this paper we study the influence of the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits of an electron on transmission features in single barrier structures. Within the parabolic conduction-band approach, a modified one-dimensional effective-mass Schr?dinger equation, including the magneto-coupling effect generated from the position-dependent effective mass of the electron, is strictly derived. Numerical calculations for single barrier structures show that the magneto-coupling effect brings about a series of the important changes for the transmission probability, the above-barrier quasi-bound states, and the tunneling time. Through examining the variation of the above-barrier resonant-transmission spectrum with the barrier width and observing the well-defined Lorentzian line-shape of the above-barrier resonant peaks, we convincingly show that the above-barrier resonant transmission in single barrier structures is delivered by the above-barrier quasibound states in the barrier region, just as the below-barrier resonant tunneling in double barrier structures is mediated by the below-barrier quasi-bound states in the well. Furthermore, we come to the conclusion that the magneto-coupling effect brings about not only the splitting of the above-barrier quasi-bound levels but also the striking reduction of the level-width of the quasi-bound states, correspondingly, the substantial increase of the density of the quasi-bound states. We suggest that magneto-coupling effects may be observed by the measurements of the optical absorption spectrum associated with the above-barrier quasi-bound states in the single barrier structures. Received: 26 September 1997 / Revised: 26 November 1997 / Accepted: 15 December 1997     

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.     

The statistical integrals of bound and quasi-bound states of gas phase complexes formed by symmetrical nonpoint monomers

Equations for calculations of the statistical integrals of bound and quasi-bound weak binary complex states in the gas phase are extended to nonpoint monomers. The equations for states of both types are derived using a unified approach different from those reported earlier. The equations can be used for estimating the thermodynamic functions, equilibrium constants, and concentrations of weakly bound complexes in the ideal gas state and for verifying the results of numerical simulation of association processes in the gas phase.     

A chiral quark model for meson electroproduction in the S11 partial wave

We calculate the meson scattering and electroproduction amplitudes in the S11 partial wave in a coupled-channel approach that incorporates quasi-bound quark-model states. Using the quark wave functions and the quark-meson interaction from the Cloudy Bag Model, we obtain a good overall agreement with the available experimental results for the partial widths of the N(1535) and the N(1650) resonances as well as for the pion, eta and kaon electroproduction amplitudes. Our model is consistent with the N(1535) resonance being dominantly a genuine three-quark state rather than a quasi-bound state of mesons and baryons.     

Pair density wave in the pseudogap state of high temperature superconductors

Recent scanning tunneling microscopy experiments of Bi(2)Sr(2)CaCu(2)O(8+delta) have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [Science 303, 1995 (2004)]]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper pairs without global phase coherence. We show that scanning tunneling microscopy measurements can distinguish a pair density wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an on site periodic potential.     

Influence of different band masses on ballistic charge transport in ferromagnet–superconductor–ferromagnet trilayers

We study transport properties of clean FISIF double-barrier junctions consisting of metallic or semiconducting ferromagnets (F), a superconductor (S), and insulating interfaces (I). We solve the scattering problem based on the Bogoliubov–de Gennes equation and calculate differential conductance for arbitrary interface transparency, different effective band masses and Fermi wave vectors in the conductors. We analyze size and coherence effects that characterize ballistic transport: subgap transmission and geometrical oscillations of the conductance. We find that different band masses, as well as different Fermi wave vectors, affect the transport properties in a way similar to interfaces of a finite transparency. In all these cases, charge transport is reduced to resonant tunneling through the quasi-bound states in the superconducting film.     

Resonant tunneling,eigenvalue and energy band calculation for potential and periodic potential structures

Recursion formulae for the reflection and the transmission probability amplitudes and the eigenvalue equation for multistep potential structures are derived. Using the recursion relations, a dispersion equation for periodic potential structures is presented. Some numerical results for the transmission probability of a double barrier structure with scattering centers, the lifetime of the quasi-bound state in a single quantum well with an applied field, and the miniband of a periodic potential structure are presented.     

Resonant tunneling mediated by resonant emission of intersubband plasmons

We study tunneling through resonant tunneling diodes (RTD) with very long emitter drift regions (up to 2 microm). In such diodes, charge accumulation occurs near the double barrier on the emitter side, in a self-induced potential pocket. This leads to a substantial enhancement of the wave function overlap between states of the pocket and the RTD, and, consequently, to increased off-resonant current mediated by various scattering processes. For RTD with the longest drift region (2 microm), an additional strong current peak is observed between the first and the second resonant peaks. We attribute this pronounced feature to the intersubband transitions mediated by resonant emission of intersubband plasmons.     

Role of elastic scattering in electron dynamics at ordered alkali overlayers on Cu(111)

Scanning tunneling spectroscopy of p(2 x 2) Cs and Na ordered overlayers on Cu(111) reveals similar line widths of quasi-two-dimensional quantum well states despite largely different binding energies. Detailed calculations show that 50% of the line widths are due to electron-phonon scattering while inelastic electron-electron scattering is negligible. The mechanism of enhanced elastic scattering due to Brillouin zone backfolding contributes the remaining width.     

Band offsets, Fermi levels and impurity bands in doped contact layers

A mathematical formalism for use in the study of the temperature dependence of Tsu-Esaki tunneling currents is developed. The discussion includes recently discovered corrections to the Tsu-Esaki tunneling current calculation. These corrections involve emitter and collector electron density effects. The tunneling current is fully amenable to numerical calculation, but some calculations can be facilitated by analytic techniques. An operator technique of Blankenbecler is illustrated and used to generate low temperature series expansions for the tunneling current and emitter-collector electron densities.     

Exact integral operator form of the Wigner distribution-function equation in many-body quantum transport theory

A formal derivation of a generalized equation of a Wigner distribution function including all many-body effects and all scattering mechanisms is given. The result is given in integral operator form suitable for application to the numerical modeling of quantum tunneling and quantum interference solid state devices. In the absence of scattering and many-body effects, the result reduces to the noninteracting-particle Wigner distribution function equation, often used to simulate resonant tunneling devices. The derivation uses a Weyl transform technique which can easily incorporate Bloch electrons. Weyl transforms of self-energies are derived. Various simplifications of a general quantum transport equation for semiconductor device analysis and self-consistent numerical simulation of a quantum distribution function in the phase-space/frequency-time domain are discussed. Recent attempts to include collisions in the Wigner distribution-function approach to the numerical simulation of tunneling devices are clearly shown to be non-self-consistent and inaccurate; more accurate numerical simulation is needed for a deeper understanding of the effects of collision and scattering.     

Carrier kinetics and population inversion in Landau level system in cascade GaAs/AlGaAs quantum well structures

The carrier distribution over Landau levels was studied in resonant tunneling GaAs/AlGaAs quantum well structures under tunneling pumping of the upper subband. The numerical calculations of the Landau levels population for various values of pumping intensity (tunneling time), magnetic field and the structure doping were carried out. The effect of various scattering mechanisms, as two-electron (electron–electron scattering) as single-electron (acoustic phonon and interface roughness scattering) ones on level population was studied. The population inversion between the zeroth Landau level of the upper subband and the first Landau level of the lowest subband was shown to exist in wide range of the magnetic field strength thus providing the possibility of wide range tunable stimulated terahertz emission.     

Abrupt turn-on and hysteresis in a VCSEL with frequency-selective optical feedback

The emission characteristics of a vertical-cavity surface-emitting laser (VCSEL) operated in a single-transverse mode and coupled to an external cavity with a diffraction grating as a frequency-selective element are analyzed experimentally, numerically and analytically. The experiments yield a rather abrupt turn-on of the VCSEL to a high-amplitude emission state and hysteresis phenomena. The experimental results are explained by numerical simulations and analytical calculations demonstrating the possibility of bistability between lasing and non-lasing states close to threshold. Hence, the scheme might be useful in all-optical photonic switching applications. A detailed bifurcation analysis near threshold is given by superimposing the numerical results with analytical steady-state curves. The mode selection and switching behavior obtained in the simulations can be interpreted from the point of view of the preference of states with the minimal total losses.     

结构和磁场对三势垒结构中共振隧穿时间的影响(英文)

为了理解在三势垒结构中准束缚能级Ez和隧穿寿命对磁场的依赖性,采用传输矩阵的方法研究了在三势垒结构中的共振隧穿过程。分别研究了在三势垒结构中的透射几率特征和隧穿寿命。结果表明:随着中间势垒厚度L的增加,第一准束缚能级E1z增加,而第二准束缚能级E2z却减小。随着磁场强度B和朗道量子数n的增加,与第一和第二准束缚能级(E1z,E2z)对应的寿命τ缩短。对于B=15和n=15的情况,L对τ的影响很小。     

The effect of the crystal structure of the field emitter on field ion energy distributions

The field ionization probability of an atom as a function of distance from the field emitter is discussed in terms of the atomic arrangement and the electron scattering properties of the ion cores of the emitter in the immediate neighborhood of the atom to be ionized, and the electron transmission properties of the potential barrier between the emitter and that atom. This approach to field ionization calculations is somewhat similar to field ionization calculations based on low energy electron diffraction (LEED) procedure in that it takes into account electron scattering from the first few atomic layers of the emitter. It differs from LEED type calculations, because it considers the highly localized nature of the ionization near a surface atom. This localization makes the ionization probability relatively insensitive to the two-dimensional periodicity of the emitter surface. A one-dimensional calculation, in which only the potential barrier and three ion core scatterers in line with the field are considered, shows secondary structure in the predicted field ion energy distributions near the critical energy deficit, as well as the well known, primary field induced resonance peaks. The surface orientation dependence of these distributions arises naturally from this model because the secondary structure depends strongly upon the crystal parameter along a line parallel to the field. This one-dimensional calculation can be no more than an approximation to a complete calculation. It is interesting, however, that such a simple physical model, in which scattering from the image potential and only two or three ion cores is considered, rather than scattering from a complete crystal, can give prodicted field ion onergy distributions which are similar to those experimentally observed.     

Carrier dynamics and stimulated radiative terahertz transitions between Landau levels in cascade GaAs/AlGaAs quantum well structures

The carrier distribution over Landau levels was studied in resonant tunneling GaAs/AlGaAs quantum well structures under tunneling pumping of the upper subband. The numerical calculations of the Landau level populations for various values of pumping intensity (tunneling time), magnetic field and structure doping were carried out. The population inversion between zeroth Landau level of the upper subband and the first Landau level of the lowest subband was shown to exist in wide range of the magnetic field strength. The effect of various scattering mechanisms, both two-particle (electron-electron scattering) and single-particle (acoustic phonon and interface roughness scattering) ones, on level population was studied. The way of lifting the selection rule forbidding the inter-Landau level terahertz transitions of interest and achieving considerable values of the dipole matrix element is proposed.     

Spontaneous emission enhancement in metal-dielectric metamaterials

We study the spontaneous emission of a dipole emitter imbedded into a layered metal-dielectric metamaterial. We demonstrate ultra-high values of the Purcell factor in such structures due to a high density of states with hyperbolic isofrequency surfaces. We reveal that the traditional effective-medium approach greatly underestimates the value of the Purcell factor due to the presence of an effective nonlocality, and we present an analytical model which agrees well with numerical calculations.     

A theoretical study of resonant tunneling characteristics in triangular double-barrier diodes

Resonant tunneling characteristics of triangular double-barrier diodes have been investigated systematically in this Letter, using Airy function approach to solve time-independent Schrödinger function in triangular double-barrier structures. Originally, the exact analytic expressions of quasi-bound levels and quasi-level lifetime in symmetrical triangular double-barrier structures have been derived within the effective-mass approximation as a function of structure parameters including well width, slope width and barrier height. Based on our derived analytic expressions, numerical results show that quasi-bound levels and quasi-level lifetime vary nearly linearly with the structure parameters except that the second quasi-level lifetime changes parabolically with slope width. Furthermore, according to our improved transmission coefficient of triangular double-barrier structures under external electric field, the current densities of triangular double-barrier diodes with different slope width at 0 K have been calculated numerically. The results show that the N-shaped negative differential resistance behaviors have been observed in current–voltage characteristics and current–voltage characteristics depend on the slope width.     

Tunable quantum dot arrays formed from self-assembled metal-organic networks

The confinement of Ag(111) surface-state electrons by self-assembled, nanoporous metal-organic networks is studied using low-temperature scanning tunneling microscopy and spectroscopy as well as electronic structure calculations. The honeycomb networks of Co metal centers and dicarbonitrile-oligophenyl linkers induce surface resonance states confined in the cavities with a tunable energy level alignment. We find that electron scattering is repulsive on the molecules and weakly attractive on Co. The tailored networks represent periodic arrays of uniform and coupled quantum dots.     

Transformation-matrix method for tunnel-effect simulation

The problem of numerically simulating steady-state scattering and the tunneling transfer of electrons was considered for a 1D potential barrier with an arbitrary shape. An effective numerical approach to solving this problem was developed on the basis of the transformation-matrix method. To test this approach, a computer program was written and applied to calculations of the tunneling processes. The convergence of the method proposed was further investigated in numerical experiments.