Single and double spin asymmetries in the elastic <Emphasis Type="Italic">e</Emphasis>-<Emphasis Type="Italic">d</Emphasis> scattering and their dependence on the deuteron wave function

Single and double spin asymmetries in the elastic electron-deuteron (e-d ) scattering were investigated. The tensor-deuteron asymmetries T_2i(i = 0, 1, 2) and the beam-vector-deuteron asymmetries T ^e _1i(i = 0, 1) were calculated and compared with the available experimental data. The sensitivity of the results for these spin asymmetries to the deuteron wave function has been investigated. The predicted asymmetries were found to be agree with one another and with experiment. It was found that, the double spin asymmetry T ^e ₁₀ is much smaller than the T ^e ₁₁-asymmetry. Therefore, in addition to the single tensor-deuteron asymmetry T₂₀, the doubly beam-vector-deuteron asymmetry T ^e ₁₁ can be used as an another tool for extracting the deuteron electromagnetic form factors.     

Microwave photoresistance of a two-dimensional electron gas in a ballistic microbar

The effect of millimeter microwave radiation on the electron transport of two-dimensional (2D) ballistic microbars formed on the basis of individual GaAs quantum wells at a temperature of T = 4.2 K in magnetic fields B < 0.6 T has been investigated. Differences have been revealed in the magnetic field dependences of the microwave photoresistance of a 2D electron gas in Hall bars with a length L and a width W for the cases L, W > l _p and L, W < l _p , where l _p is the electron mean free path for momentum. The microwave photoresistance in macroscopic bars (L, W > l _p ) is a periodic alternating function of the inverse magnetic field; in microbars (L, W < l _p ), it is a periodic positive function of 1/B. The experimental results indicate that the mechanisms of the microwave photoresistance of a 2D electron gas are different for macroscopic and microscopic bars.     

Gaussian free field in the background of correlated random clusters,formed by metallic nanoparticles

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T ? T _c . The fractal dimension of iso-potential lines (D _f ), the exponent of the distribution function of the gyration radius (τ _r ), and the loop lengths (τ _l ), and also the exponent of the loop Green function x _l change in terms of T ? T _c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D _f (T) ? D _f (T _c ) ~ 1/√ξ(T), in which ξ(T) is the spin correlation length in the Ising model.     

Superconductor-insulator transition tuned by annealing in Bi-film on top of Co-clusters

We deposited amorphous Bi films with a thickness between 3 and 6.5 nm at 4.2 K on top of previously deposited Co clusters having a mean size of ～4.5 nm. The Co cluster layers thickness was between 2.3 and 5 nm. In-situ electrical transport measurements were performed between 2 and 100 K. Measurements on as-prepared samples having a Bi layer thickness of 3.0 nm show hopping (tunneling) conductivity as σ(T) = σ ₀ exp[?(T ₀/T)^1/2] above the superconducting transition temperature T _C and re-entrance behavior again with hopping (tunneling) conductivity below T _C . Annealing of films having a Bi layer thickness of 5.5 nm results in a decrease of resistivity, with variable-range hopping conduction behavior as σ(T) = σ ₀ exp[?(T ₀/T)^1/3 ]. Quite different are the findings for films having a Bi layer thickness of 6.5 nm: annealing of these films results in a power-law behavior as σ(T) = σ ₀ T ^α with α = 2/3, indicating that these films are close to a quantum critical point separating superconducting and insulating phases. A phase diagram including all experimental observations is proposed.     

Role of initial correlation in coarsening of a ferromagnet

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of theIsing model, employing the Glauber spin-flip mechanism, in space dimensionsd = 2 and3, on square and simplecubic lattices. Results for the persistence probability and the domain growth arediscussed for quenches to various temperatures (T _f ) below the criticalone (T _c ), from differentinitial temperatures T _i ≥T _c . In long timelimit, for T _i >T _c ,the persistence probability exhibits power-law decay with exponents θ ? 0.22 and? 0.18 in d = 2 and 3, respectively. For finite T _i , the early timebehavior is a different power-law whose life-time diverges and exponent decreases asT _i →T _c . The two steps areconnected via power-law as a function of domain length and the crossover to the secondstep occurs when this characteristic length exceeds the equilibrium correlation length atT =T _i . T _i =T _c is expected toprovide a new universality class for which we obtain θ ≡θ _c ? 0.035 ind = 2 and?0.105 in d = 3. The time dependenceof the average domain size ?, however, is observed to be rather insensitive tothe choice of T _i .     

The structure of a vortex line and the lower critical field in superconducting alloys

The structure of an isolated vortex line, and the lower critical fieldH _c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT _c . The free energy functional including the corrections of order [1?(T/T _c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1?(T/T _c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ ₀ /l) (whereξ ₀ is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T _c forκ=1 andα=0). The ratioH _c1/H _c (where the thermodynamic criticalH _c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH _c 1/H _c is always less than 3% for arbitrary values ofκ andα asT decreases fromT _c to 0.9T _c ).     

Variable-range cotunneling and conductivity of a granular metal

The Efros-Shklovskii (E-S) law for the conductivity of granular metals is interpreted as a result of a variable-range cotunneling process. The cotunneling between distant resonant grains is predominantly elastic at low T ≤ T _c , while it is inelastic (i.e., accompanied by creation of electron-hole pairs on a string of intermediate non-resonant grains) at T ≥ T _c . The corresponding E-S temperature T _ES , in the latter case, is slightly (logarithmically) T dependent. The magnetoresistance in the two cases is different: it may be relatively strong and negative at T?T _c , while, at T > T _c , it is suppressed due to inelastic processes, which destroy the interference.     

Magnetization and Static Magnetic Susceptibility of Fine-Crystalline High-Temperature YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> Superconductors Synthesized by the Sol–Gel Method

A comparative study of the magnetization and static magnetic susceptibility of high-temperature superconductors (HTSC) YBa₂Cu₃O_y synthesized by two variants of the sol–gel method with different average sizes of crystallites 〈 D〉 ranging 0.4–2 μm has been performed in constant magnetic fields (Н ≤ 6 kOe). It has been shown that the different annealing temperatures and times, at which their crystal structure is formed, change both the average sizes of crystallites 〈D〉 and the sizes of the structural homogeneity regions 〈l〉 and, at the same time, the magnetic field penetration depth (λ) and the coherence length (ξ). As a result, such parameters as 〈D〉 ~ λ and 〈l〉 ~ ξ become comparable, leading to a change in the physical characteristics of HTSCs. It has also been shown that the superconducting transition temperature T_c determined from the measurements of magnetic characteristics in constant magnetic fields remains within values optimal for superconductivity (T_c ≈ 92 K) in the case of an optimal number (y) of oxygen atoms, which determine the levels of charge doping for a given compound.     

Variable-range hopping conduction in LaMnO<Subscript>3 + δ</Subscript>

The temperature dependence of the electrical resistivity ρ(T) for ceramic samples of LaMnO_{3 + δ} (δ = 0.100–0.154) are studied in the temperature range T = 15–350 K, in magnetic fields of 0–10 T, and under hydrostatic pressures P of up to 11 kbar. It is shown that, above the ferromagnet-paramagnet transition temperature of LaMnO_{3 + δ}, the dependence ρ(T) of this compound obeys the Shklovskii-Efros variable-range hopping conduction: ρ(T) = ρ₀(T)exp[(T ₀/T)^1/2], where ρ₀(T) = AT ^9/2 (A is a constant). The density of localized states g(?) near the Fermi level is found to have a Coulomb gap Δ and a rigid gap γ(T). The Coulomb gap Δ assumes values of 0.43, 0.46, and 0.48 eV, and the rigid gap satisfies the relationship γ(T) ≈ γ(T _v)(T/T _v)^1/2, where T _v is the temperature of the onset of variable-range hopping conduction and γ(T _v) = 0.13, 0.16, and 0.17 eV for δ = 0.100, 0.125, and 0.154, respectively. The carrier localization lengths a = 1.7, 1.4, and 1.2 Å are determined for the same values of δ. The effect of hydrostatic pressure on the variable-range hopping conduction in LaMnO_{3 + δ} with δ = 0.154 is analyzed, and the dependences Δ(P) and γ_v(P) are obtained.     

Notes on number density fluctuations and the scattering cross section for electromagnetic waves scattered from a thermal nonequilibrium plasma

The scattering cross section and the Doppler spectrum for electromagnetic waves scattered by the electron density fluctuations of a plasma, where the mean kinetic temperature of the electronsT _e may differ from that of the ionsT _i , has been obtained among others byFejer, Buneman, Renau, Camnitz andFlood, andSalpeter. These authors use different methods of approach to calculate the autocovariance of the electron number-density fluctuations (from the mean) and then obtain the scattering cross section. Because of the differing results, the methods, concepts, and derivations of the scattering cross section are carefully examined in this paper. It is shown that the short-time dynamical considerations incorporated in the formulation of the statistical theory of the electron number-density fluctuations of the plasma as used by several authors (for instanceFejer, Buneman, Salpeter,) leads to results of limited validity. In addition, a fundamental error in calculating the electron density fluctuations leads these latter authors to an incorrect scattering cross section. The theory of scattering of electromagnetic waves from a plasma, where the electrons arenot in thermal equilibrium with the ions but statistical equilibrium exists, is developed in a general way. The covariance of the number-density fluctuations from the mean of the charged species of the plasma and the scattering cross sectionσ(q) are obtained. In particular it is shown that for a wavelength λ much greater than the effective Debye lengthd, the backscattering cross section increases and approaches complete incoherent scattering asT _e /T _i increases. This result is explained by noting that in the case of thermal equilibrium, the predicted value of the back-scattering cross section is smaller than that of the backscattering cross section from completely uncorrelated electron density fluctuations because the electrostatic interaction between the charged particles of the plasma, which is a function ofT _e andT _i , introduces a certain amount of organization in otherwise completely uncorrelated electron density fluctuations. When the mean temperature of the electrons increases relative to that of the ions, the organization introduced in the fluctuations diminishes because of the increasing thermal agitation of the electrons relative to that of the ions, and the backscattering process approaches that of incoherent backscattering (Thomson-type scattering). The spectrum function of incoherent scattering of electromagnetic waves from a nonequilibrium plasma is obtained and some cases of current interest are plotted.     

Scaling of the conductance and resistance of square lattices with an exponentially wide spectrum of the resistances of links

The conductance G? and \(\overline {{G^{ - 1}}} \) resistance average over realizations of disorder have been calculated for various sizes of square lattices L. In contrast with different direction of change in the two quantities at percolation in lattices with the binary spread of conductances of links (g _i = 0 or 1), it has been found that the mean conductance and resistance of lattices decrease simultaneously with an increase in L in the case of an exponential distribution of local conductances g _i = exp(?kx_i), where x _i ∈ [0,1] are random numbers. When L is smaller than the disorder length L₀ = bk^v, G?(L) and \(\overline {{G^{ - 1}}} \)(L) are proportional to L^?n with n = k/5 and k/6, respectively. A similar behavior is characteristic of the distributions of conductances of links, which simulate a transition between the open and tunneling regimes in semiconducting lattices of antidots created in a two-dimensional electron gas.     

Temperature dependence of the upper critical field of superconducting alloys

The upper critical field,H _c2, is calculated in the temperature range close toT _c for arbitrary values of the mean free path 1. The method is to treat the fourth-order term in the linearized differential equation for the gap parameter as a perturbation to the harmonic oscillator equation. The Nambu-Tuan term, which determines the structure of the “clean-limit” and “dirty-limit” parts of the fourth-order term, is calculated by means of the ladder diagram technique for impurity interaction lines. The result is that the magnitude of the slope of the curveH _c2/√2H _c κ versust=T/T _c att=1 decreases monotonically from the value 0.41 to 0.12 as the ratio of the BCS coherence lengthξ ₀ to the mean free path 1 increases from 0 to ∞. For 1?ξ ₀ this slope is about 0.26.     

Zur Supraleitung von Schichtpaketen aus Normal- und Supraleitern

Superimposed films of a super- and a normalconducting metal are produced on a quartz plate by evaporation. In most cases lead and occasionally also tin is used as superconductor. The normal metals are copper, manganese and chromium. For more than 50 samples of different combinations the transitiontemperatures are measured. The mean free path of the electrons for the metals can be varied by the conditions of condensation. By means of a phenomenological theory, which we owe in principle to a discussion with ProfessorFröhlich, Liverpool, we succeed in formulating expressions fort=f(D _s ,D _n ,l _s ,l _n ,ξ₀).D,l andξ ₀ are the thickness, mean free path and the coherence length of the supra- or the normal metals andt is the reduced transitiontemperature. The developed equations can be well fitted to the measured data also to those of other authors.     

Thermoelectric effect in the Kondo dot side-coupled to a Majorana mode

We investigate the linear thermoelectric response of an interacting quantum dot side-coupled by one of two Majorana modes hosted by a topological superconducting wire. We employ the numerical renormalization group technique to obtain the thermoelectrical conductance L in the Kondo regime while the background temperature T, the Majorana-dot coupling Γ _m , and the overlap ε _m between the two Majorana modes are tuned. We distinguish two transport regimes in which L displays different features: the weak- (Γ _m <T _K ) and strong-coupling (Γ _m >T _K ) regimes, where T _K is the Kondo temperature. For an infinitely long nanowire where the Majorana modes do not overlap (ε _m = 0), the thermoelectrical conductance in the weak-coupling regime exhibits a peak at T ~ Γ _m <T _K . This peak is ascribed to the anti-Fano resonance between the asymmetric Kondo resonance and the zero-energy Majorana bound state. In the strong-coupling regime, on the other hand, the Kondo-induced peak in L is affected by the induced Zeeman splitting in the dot. For finite but small overlap (0 <ε _m <Γ _m ), the interference between the two Majorana modes restores the Kondo effect in a smaller energy scale Γ′ _m and gives rise to an additional peak in Γ ~ Γ′ _m, whose sign is opposite to that at T ~ Γ _m . In the strong-coupling regime this additional peak can cause a non-monotonic behavior of L with respect to the dot gate. Finally, in order to identify the fingerprint of Majorana physics, we compare the Majorana case with its counterpart in which the Majorana bound states are replaced by a (spin-polarized) ordinary bound state and find that the thermoelectric features for finite ε _m are the genuine effect of the Majorana physics.     

Extraordinary photons with unusual angular momentum

A series of novel state-vector functions (SVFs), which is the general solution of the Schrödinger equation for a photon, are constructed. Each set of these functions consists of a triplet of eigen-SVFs: The triplet can be broken down into a pair of nonzero l-order functions and a single zero-order function. The photons, described with a triplet of eigen-SVFs, possess all the quantum characteristics of a photon: In addition to common attributes like energy E = ? _ω , and momentum p _z = ? _κ , they also exhibit different angular momenta (AM) L _z+ = l?, L _z? = l?, and L _z0 = 0, where l?1. In other words, in addition to usual eigenvalues L _z±= ±?, there are unusual nonzero l-order eigenvalues L _z± = ±l? and a zero-order eigenvalue L _z0 = 0 for AM of a photon. By a series of SVFs, the pattern from nonzero l-order and zero-order Laguerre-Gaussian modes of a laser beam is explained well from a quantum mechanical point of view.     

Rare meson decay in supersymmetric theory with nonconservation of <Emphasis Type="Italic">R</Emphasis>-parity

The decay of mesons K ⁺ → π ^? l ⁺ l′⁺ and D ⁺ → K ^? l ⁺ l′⁺ (l, l′ = e, μ) involving a change of lepton number ΔL = 2 is considered in a supersymmetric extension of the standard model in which R-parity is not conserved due to trilinear Yukawa interactions. The obtained estimates for the probabilities of these decays are significantly lower than the direct experimental upper limits.     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

Electron–phonon heat exchange in quasi-two-dimensional nanolayers

We study the heat power P transferred between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes. The temperature range is typically below 1 K, such that the wavelengths of the excited phonon modes in the system is large enough so that the picture of a quasi-two-dimensional phonon gas is applicable. Moreover, due to the quantization of the components of the electron wavevectors perpendicular to the metal film’s surface, the electrons spectrum forms also quasi two-dimensional sub-bands, as in a quantum well (QW). We describe in detail the contribution to the electron–phonon energy exchange of different electron scattering channels, as well as of different types of phonon modes. We find that heat flux oscillates strongly with thickness of the film d while having a much smoother variation with temperature (T _e for the electrons temperature and T _ph for the phonons temperature), so that one obtains a ridge-like landscape in the two coordinates, (d, T _e ) or (d, T _ph ), with crests and valleys aligned roughly parallel to the temperature axis. For the valley regions we find P ∝ T _e ^3.5 – T _ph ^3.5 . From valley to crest, P increases by more than one order of magnitude and on the crests P cannot be represented by a simple power law. The strong dependence of P on d is indicative of the formation of the QW state and can be useful in controlling the heat transfer between electrons and crystal lattice in nano-electronic devices. Nevertheless, due to the small value of the Fermi wavelength in metals, the surface imperfections of the metallic films can reduce the magnitude of the oscillations of P vs. d, so this effect might be easier to observe experimentally in doped semiconductors.