Landau-level lifetimes in PbTe nipi superlattices, PbTe/PbEuTe and InAs/AlSb quantum wells

Landau-level lifetimes are determined from saturation cyclotron resonance (CR) in wide parabolic wells, quantum wells and bulk PbTe–Pb_1−xEu_xTe systems. These narrow gap structures exhibit strong band non-parabolicity necessary to terminate the normally equi-spaced Landau-level ladder. It was not possible to saturate the bulk sample, but short lifetimes, of between 1.5 and 8 ps, were obtained for the wide parabolic well and the quantum well, respectively, utilising a multi-level rate equation model. We also report the first pump–probe cyclotron resonance result in an InAs–AlSb quantum structure. The pump–probe experiment provides a direct determination of the lifetime, giving τ=40 ps in this InAs–AlSb sample. This shows good agreement with an 8×8k·p calculation.     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Zeeman effect and magnetic anomalies in narrow-gap semiconductor quantum dots

We present a systematic theoretical study, based on the Kane–Weiler 8×8 k·p model, of the linear Zeeman splitting introduced by the interaction between the angular momentum and the magnetic field which can give a measure of the non-linear Zeeman effect associated with interband coupling and diamagnetic contributions. The conduction and valence bands g-factors are calculated for InSb spherical and semi-spherical quantum dots. The calculations of the g-factors showed an almost linear dependence, for the ground state, on the magnetic field. We have also found that the strong magnetic field dependence as well as the dependence on the dot size of the effective spin splitting can be unambiguously attributed to the strength of the inter-level mixing.     

Curved two-dimensional electron gases

A method is introduced which makes it possible to fabricate non-planar two-dimensional electron gases. Making use of the “epitaxial lift-off” process, patterned, gated and contacted heterostructures are transferred from their crystalline substrate onto small glass tubes with diameters of a few millimeters. The transport properties of two-dimensional electron gases inside these curved semiconductor films are characterized by low-temperature magnetoresistance measurements. In the longitudinal resistance we find weak Shubnikov–de Haas oscillations, which are periodic in B⁻¹. The transverse resistance exhibits well-developed quantum Hall plateaus at low magnetic fields. At high fields, we observe a pronounced breakdown of the Hall effect. The experimental results are compared with simple theoretical models.     

Steady-state heat conduction in quiescent fluids: Incompleteness of the Navier-Stokes-Fourier equations

Linear irreversible thermodynamic principles are used to demonstrate, by counterexample, the existence of a fundamental incompleteness in the basic pre-constitutive mass, momentum, and energy equations governing fluid mechanics and transport phenomena in continua. The demonstration is effected by addressing the elementary case of steady-state heat conduction (and transport processes in general) occurring in quiescent fluids. The counterexample questions the universal assumption of equality of the four physically different velocities entering into the basic pre-constitutive mass, momentum, and energy conservation equations. Explicitly, it is argued that such equality is an implicit constitutive assumption rather than an established empirical fact of unquestioned authority. Such equality, if indeed true, would require formal proof of its validity, currently absent from the literature. In fact, our counterexample shows the assumption of equality to be false. As the current set of pre-constitutive conservation equations appearing in textbooks are regarded as applicable both to continua and noncontinua (e.g., rarefied gases), our elementary counterexample negating belief in the equality of all four velocities impacts on all aspects of fluid mechanics and transport processes, continua and noncontinua alike.     

The ν1 and ν3 stretching fundamental bands of PD3

The infrared (IR) spectrum of PD₃ has been recorded in the 1580–1800 cm⁻¹ range at a resolution of 0.0027 cm⁻¹. About 2400 rovibrational transitions with J^′=K^′22 have been measured and assigned to the ν₁ (A₁) and ν₃ (E) stretching fundamentals. These include 506 “perturbation-allowed” transitions with selection rules Δ(k−l)=±3. Splittings of the K^′′=3 lines have been observed. Effects of strong perturbations are evident in the spectrum. Therefore the rovibrational Hamiltonian adopted for the analysis explicitly takes into account the Coriolis and k-type interactions between the v₁=1 and v₃=1 states, and includes also several essential resonances within these states. The rotational structure in the v₁=1 and v₃=1 vibrational states up to J^′=K^′=18 was reproduced by fitting simultaneously all experimental data. Thirty-four parameters reproduced 1950 transitions retained in the final cycle with a standard deviation of the fit equal to 4.9 × 10⁻⁴ cm⁻¹ (about the precision of the experimental measurements).     

Growth and studies of Hg1−xCdxTe based low dimensional structures

The band structure of HgTe quantum wells (QWs) has been determined from absorption experiments on superlattices in conjunction with calculations based on an 8×8 k·p model. The band structure combined with self-consistent Hartree calculations has enabled transport results to be quantitatively explained.Rashba spin–orbit, (SO) splitting has been investigated in n-type modulation doped HgTe QWs by means of Shubnikov–de Haas oscillations (SdH) in gated Hall bars. The heavy hole nature of the H1 conduction subband in QWs with an inverted band structure greatly enhances the Rashba SO splitting, with values up to 17 meV.By analyzing the SdH oscillations of a magnetic two-dimensional electron gas (2DEG) in modulation-doped n-type Hg_1−xMn_xTe QWs, we have been able to separate the gate voltage-dependent Rashba SO splitting from the temperature-dependent giant Zeeman splitting, which are of comparable magnitudes. In addition, hot electrons and Mn ions in a magnetic 2DEG have been investigated as a function of current.Nano-scale structures of lower dimensions are planned and experiments on sub-micrometer magneto-transport structures have resulted in the first evidence for ballistic transport in quasi-1D HgTe QW structures.     

The Multidimensional Filter Diagonalization Method: I. Theory and Numerical Implementation

The theory and numerical aspects of the recently developed multidimensional version of the filter diagonalization method (FDM) are described in detail. FDM can construct various “ersatz” or “hybrid” spectra from multidimensional time signals. Spectral resolution is not limited by the time-frequency uncertainty principle in each separate frequency dimension, but rather by the total joint information content of the signal, i.e., N_total = N₁ × N₂ × × N_D, where some of the interferometric dimensions do not have to be represented by more than a few (e.g., two) time increments. It is shown that FDM can be used to compute various reduced-dimensionality projections of a high-dimensional spectrum directly, i.e., avoiding construction of the latter. A subsequent paper (J. Magn. Reson. 144, 357–366 (2000)) is concerned with applications of the method to 2D, 3D, and 4D NMR experiments.     

Line strength measurements of carbonyl sulfide (OCS) in the 2v3, v1+2v2+v3, and 4v2+v3 bands

To support planetary studies of the Venus atmosphere, we measured line strengths of the 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ bands of the primary isotopologue of carbonyl sulfide (¹⁶O¹²C³²S), whose band centers are located at 4101.387, 3937.427, and 4141.212 cm⁻¹, respectively. For this, infrared absorption spectra in normal carbonyl sulfide (OCS) sample gas were recorded at an unapodized resolution of 0.0033 cm⁻¹ at ambient room temperatures using a Bruker Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory. The FTS instrumental line shape (ILS) function was investigated, which revealed no significant instrumental line broadening or distortions. Various custom-made short cells and a multi-pass White cell were employed to achieve optical densities sufficient to observe the strong 2v₃ and the weaker bands in the region. Gas sample impurities and the isotopic abundances were determined from mass spectrum analysis. Line strengths were retrieved spectrum by spectrum using a non-linear curve fitting algorithm adopting a standard Voigt line profile, from which Herman–Wallis factors were derived for the three bands. The band strengths of 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ of ¹⁶O¹²C³²S (normalized at 100% of isotopologue) are observed to be 6.315(13)×10⁻¹⁹, 1.570(2)×10⁻²⁰, and 7.949(20)×10⁻²¹ cm⁻¹/molecule cm⁻², respectively, at 296 K. These results are compared with earlier measurements and the HITRAN 2004 database.     

Large amplitude spin waves in ultra-cold gases

We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. The full position and momentum dependence of the distribution function must then be retained. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves (or internal conversion) in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped ⁸⁷Rb atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence. In two appendices we calculate the Wigner transform of the interaction term in the S matrix method, to first order in gradients; Appendix A.1 treats the case of spin-independent interactions, Appendix A.2 that of spin-dependent interactions.Received: 17 April 2003, Published online: 17 July 2003PACS: 05.30.-d Quantum statistical mechanics - 51.10.+y Kinetic and transport theory of gases - 75.30.Ds Spin waves     

A turn-on fluorescent chemosensor for Hg based on phenanthroline fluorophore

Dipyrido[3,2-a:2′,3′-c]-phenazine (L) was employed as a selectively fluorescent chemosensor for Hg²⁺ in DMF solution under buffered conditions with its fluorescence being strongly increased. The fluorescence increasing was attributed to the formation of L–Hg²⁺ by 1:1 complex ratio (K=3.7×10⁵ M⁻¹), which constitutes the basis for the determination of Hg²⁺ with the prepared chemosensor. The experiment results also show that the response behavior of L to Hg²⁺ is pH independent in the range of pH 6.0–9.0 and show excellent sensitivity and selectivity for Hg²⁺ over other examined metal ions.     

Guidelines for choosing the transition matrix in Monte Carlo methods using Markov chains

The sampling method proposed by Metropolis et al. (J. Chem. Phys. 21 (1953), 1087) requires the simulation of a Markov chain with a specified π as its stationary distribution. Hastings (Biometrika 57 (1970). 97) outlined a general procedure for constructing and simulating such a Markov chain. The matrix P = {p_ij} of transition probabilities is constructed using a defined symmetric function s and an arbitrary transition matrix Q. With respect to asymptotic variance reduction, Peskun (Biometrika 60 (1973), 607) determined, for a given Q, the optimum choice for s_ij. Here, guidelines are given for choosing Q so that the resulting Markov chain sampling method is as precise as is practically possible. Examples illustrating the use of the guidelines, including potential applications to problems in statistical mechanics and to the problem of estimating the probability of an simple event by “hit-ormiss” Monte Carlo in conjunction with Markov chain sampling, are discussed.     

Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schrödinger equation. Using complex canonical variables, a formal proof of the quantization axiom p → pˆ = −i, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov–Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion.     

Compositionally asymmetrical multiquantum wells: “Pseudo-molecules” for giant optical nonlinearities in the infrared (9–11 μm)

Intersubband transitions in quantum well have extremely large oscillator strengths and induce strong nonlinear effects in structures where inversion symmetry is broken, realized by growing AlGaAs quantum wells with asymmetrical A1 gradients. These compositionally asymmetrical multiquantum wells may thus be viewed as giant “quasimolecules” optimized for optimal nonlinearities in the mid infrared. Optical rectification as well as second harmonic generation have been measured in those structures using a continuous CO₂ laser. At 10.6 μm the nonlinear coefficients are more than 3 orders of magnitude higher in these samples than for bulk GaAs (i.e. χ₀⁽²⁾ = 5.3 × 10⁻⁶m/V, χ_2ω⁽²⁾ = 7.2 × 10⁻⁷ m/V) and are in good agreement with theoretical predictions. We present more complex “pseudo-molecules” involving weakly coupled quantum wells. The optical rectification effects in these devices are so large χ₀⁽²⁾ = 1.6 × 10⁻³ m/V) that application to infrared detection may be envisioned.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

On search and identification of tracks due to short-lived SHE nuclei in extraterrestrial crystals

The unique approach for search and unambiguous identification of short-lived (T_1/2=10³–10⁷ years) superheavy nuclei in cosmic-ray products of the recent nucleosynthesis in our Galaxy are discussed.It is based on: (a) the ability of non-conducting crystals to register and to store for many million years the tracks due to fast nuclei with atomic number Z20 (“fossil” tracks);(b) calibrations of the said crystals with accelerated heavy ions (20Z92) and on revealing the volume etchable track length (VETL) of the fast nuclei coming to rest inside crystals—both of fossil and “fresh” tracks—to determine the charge distribution of cosmic-ray nuclei tracks and(c) the so-called “four-zone” model of tracks in crystals (and also glasses) which provides not only the VETL track length dependence for 20Z92 nuclei but also demonstrates the regular annealing behavior of VETL of 20Z92 nuclei in a broad temperature interval.This approach was first applied in the early 1980s to investigate the “fossil” tracks due to 22Z92 cosmic-ray nuclei in olivine crystals from meteorites-pallasite Marjalahti and Eagle Station.The discovery of Th–U cosmic-ray nuclei tracks in 1980 was unambiguously confirmed by calibrations of the same crystals with ²³⁸U, ¹⁹⁷Au and ²⁰⁸Pb accelerated ions in the late 1980s. More than 1600 tracks due to cosmic-ray actinide nuclei were measured during the last two decades of the 20th century.Also, 11 anomalously long tracks (track length exceeds by a factor (1.6±0.1) the track length due to Th–U nuclei were measured. The detailed analysis shows that at least 5 of these tracks could not be attributed to the Th–U nuclei. It means that now we have a preliminary proof on the existence Z110 nuclei in cosmic-rays. The abundance is Z110/Th–U=(1–3)×10⁻³ in Z110 freshly formed cosmic-rays (time interval 10³–10⁷ years).The method proposed can provide the necessary and sufficient conditions for the discovery of Z110 nuclei in nature.     

Determination of the g-factor of n-type HgTe/Hg1−xCdxTe single quantum wells

The effective g-factor of modulation doped n-type HgTe single quantum wells, SQWs, has been determined by the coincidence method in tilted magnetic fields to lie between 15 and 35. For symmetrically doped samples the effective g-factor has been found to be constant for different filling factors; however, for asymmetric SQWs, a large increase with increasing filling factor has been observed. This can be ascribed to a combination of Zeeman spin splitting and Rashba spin–orbit splitting. Reasonable agreement has been achieved between theoretical calculations based on the 8×8 k · p method and experimental results.     

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

A numerical investigation of grain-boundary grooving by means of a level set method is carried out. An idealized polycrystalline interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. Initially, the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional equation of Hamilton–Jacobi type. The results obtained are in good agreement with both Mullins analytical “small-slope” solution of the linearized problem (W. W. Mullins, 1957, j. Appl. Phys. 28, 333) (for the case of an isolated grain boundary) and with the solution for a periodic array of grain boundaries (S. A. Hackney, 1988, Scripta Metall. 22, 1731). Incorporation of an electric field changes the problem to one of electromigration. Preliminary results of electromigration drift velocity simulations in copper lines are presented and discussed.     

An “instantaneous” distribution of the ionization-passive electrons and holes under irradiation of a dielectric by intense electron or laser beams

A method is worked out for calculation of an “instantaneous” energy distribution of the ionization-passive electrons and holes resulting from the electron-electron collisions before the onset of electron-phonon relaxation under 10⁻¹⁵–10⁻¹⁴ s irradiation of a dielectric by an intense electron or laser beam. The method is based on the solution of a system of integral-differential kinetic equations of general form. The Auger and impact ionization as well as hole recoil due to the momentum conservation law are taken into account in calculations. The “instantaneous” distribution is calculated in NaCl under irradiation of the sample by a high-density electron beam. The “instantaneous” distribution of ionization-passive electrons and holes is the initial one in solutions of all kinetic equations describing further relaxation of electron excitations in irradiated materials.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 15–22, November, 2004.     

Effects of superstrings in collisions

Superstring theory in d = 10 dimensions after Calabi—Yau compactification yields a minimum low-energy gauge group SU(3)_C × SU(2)_L × U(1)_Y × U(1)_E. The low-energy theory includes particles with the quantum numbers of 27 representations of E₆, each of which contains an extra neutrino ν^c conventionally called a “right-handed neutrino”. The contributions of ν and ν^c to through Z⁰ and Z_E mixing is calculated. Small contributions are found of the new right-handed neutrino and of the superstring boson Z_E to σ(e⁺e⁻ → γ + nothing).