Temperature and purity dependence of the nuclear-spin relaxation rate in the gapless region of type-II superconductors

The volume average of the nuclear-spin relaxation rate in type-II superconductors,R _s, is calculated for magnetic fields slightly below the upper critical field and all mean free paths,l, and temperatures. It is found to be expressible solely in terms of the volume average of the density of states,\(\bar N(\omega )\), where the latter quantity has been determined recently byNeumann for alll. The derivation is based onHelfand andWerthamer's eigen-value equation for the order parameter,Δ. The deviation of\(\bar R_s \) from the relaxation rate in the normal state,R _n, is proportional to the quantity\([|\overline {\Delta |^2 } /\Delta _{BCS}^2 (T)]R_n \) (the bar denotes the spatial average). The proportionality factor is found to decrease monotonously as the temperature decreases and/orl increases. This behavior is closely related to the fact that\(\bar N(\omega )\) shows no gap for the excitation energiesω and decreases asl increases, in particular at energiesω close to zero (ω=0 corresponds to the Fermi energy).     

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.     

Singular Resonance in Fluctuation-Induced Electromagnetic Phenomena at the Rotation of a Nanoparticle near the Surface of a Condensed Medium

It has been shown that the rotation of a spherical nanoparticle with the radius R near the surface of a semi-infinite homogeneous medium can result in singular resonance in fluctuation-induced electromagnetic phenomena (Casimir force, Casimir friction, and radiative heat generation). Fluctuation electromagnetic effects increase strongly near this resonance even in the presence of dissipation in the system. The resonance occurs at distances of the particle from the surface d < d₀R(3/4ε″₁(ω₁)ε″₂ (ω₂))^1/3 (where ε″_i(ω_i) is the imaginary part of the dielectric function of the particle or the medium at the frequency of a surface phonon or plasmon polariton ω_i), when the rotation frequency coincides with poles in the photon generation rate at Ω ≈ ω₁ + ω₂. These poles are due to the multiple scattering of electromagnetic waves between the particle and surface under conditions of the anomalous Doppler effect. These poles exist even in the presence of dissipation. At d < d₀, depending on the particle rotation frequency, the Casimir force can change sign; i.e., the attraction of the particle to the surface changes to repulsion. The results can be important for the development of experimental methods for the detection of quantum friction.     

Electronic and optical properties of Fe<Subscript>2</Subscript>SiO<Subscript>4</Subscript> under pressure effect: ab initio study

We report first-principles studies the structural, electronic, and optical properties of the Fe₂SiO₄ fayalite in orthorhombic structure, including pressure dependence of structural parameters, band structures, density of states, and optical constants up to 30 GPa. The calculated results indicate that the linear compressibility along b axis is significantly higher than a and c axes, which is in agreement with earlier work. Meanwhile, the pressure dependence of the electronic band structure, density of states and partial density of states of Fe₂SiO₄ fayalite up to 30 GPa were presented. Moreover, the evolution of the dielectric function, absorption coefficient (α(ω)), reflectivity (R(ω)), and the real part of the refractive index (n(ω)) at high pressure are also presented.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

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.     

The permittivity of a monatomic gas with spatial dispersion

The longitudinal, ε^l(ω, k), and transverse, ε^tr(ω, k), permittivities of a monatomic gas were calculated. The frequency ranges in which the permittivity ε(ω) and permeability μ(ω) of a gas without spatial dispersion have a physical meaning were determined. The limiting magnetic susceptibility χ(ω) at ω=0 and the static magnetic susceptibility were found. The question of whether an electromagnetic wave with antiparallel group and phase velocities can propagate through a monatomic gas is discussed.     

Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_rf is close to the Rabi frequency ω₁ in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ? are accompanied by higher-frequency oscillations at frequencies nω_rf and nω_rf ± ?, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ? on the sign of the detuning ω₁ ? ω_rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_rf + ? increases, while the amplitude at the difference frequency ω_rf ? ? decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E′₁ centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.     

Spatial dispersion of the lattice polarizability and the properties of the large polaron

The polaron states are studied in crystals with optical phonon dispersion of the type ω²(k) = ω ₀ ² + u ² k ². The appearance and propagation of a local polarization in such a medium is treated as the evolution of a wave packet having a nonzero group velocity. This approach enables one to construct a consistent theory of moving self-trapped electron. The total energy and the effective mass of a slowly moving polaron are found and are shown to be strongly dependent on the dispersion parameter σ = u/ω₀.     

“Negative” gap in the spectrum of localized states of (In<Subscript>2</Subscript>O<Subscript>3</Subscript>)<Subscript>0.9</Subscript>(SrO)<Subscript>0.1</Subscript>

The reflection R(?ω), transmission t(?ω), absorption α(?ω), and refraction n(?ω) spectra of polycrystalline In₂O₃–SrO samples with low optical transparency, which contain In₂O₃ and In₂SrO₄ crystallites with In₄SrO_{6 + δ} interlayers, are examined. In the region of small ?ω values, the reflection coefficient decreases as the resistance of samples saturated with oxygen increases. Spectral dependences n(?ω) and α(?ω) are calculated using the classical electrodynamics relations. The results are compared to the data based on the t(?ω) spectra. The calculated absorption spectra are interpreted within the model with an overlap of tails of the density of states in the valence band and in the conduction band. A “negative” gap E _gn in the density of states with a width from–0.12 to–0.47 eV is formed in highly disordered samples in this model. It is demonstrated that the high density of defects and the band of deep acceptor states of strontium in the major matrix In₂O₃ phase are crucial to tailing of the absorption edge and its shift toward lower energies. The direct gap E _gd = 1.3 eV corresponding to the In₂SrO₄ phase is determined. The energy band diagram and the contribution of tunneling, which reduces the threshold energy for interband optical transitions, are discussed.     

Spectral Deformation for Two-Body Dispersive Systems with e.g. the Yukawa Potential

We find an explicit closed formula for the k’th iterated commutator \({\text{ad}_{A}^{k}}(H_{V}(\xi ))\) of arbitrary order k ? 1 between a Hamiltonian \(H_{V}(\xi )=M_{\omega _{\xi }}+S_{\check V}\) and a conjugate operator \(A=\frac{\mathfrak{i}}{2}(v_{\xi}\cdot\nabla+\nabla\cdot v_{\xi})\), where \(M_{\omega _{\xi }}\) is the operator of multiplication with the real analytic function ω _ξ which depends real analytically on the parameter ξ, and the operator \(S_{\check V}\) is the operator of convolution with the (sufficiently nice) function \(\check V\), and v _ξ is some vector field determined by ω _ξ . Under certain assumptions, which are satisfied for the Yukawa potential, we then prove estimates of the form \(\| {{\text{ad}_{A}^{k}}(H_{V}(\xi ))(H_{0}(\xi )+\mathfrak{i} )}\|\leqslant C_{\xi }^{k}k!\) where C _ξ is some constant which depends continuously on ξ. The Hamiltonian is the fixed total momentum fiber Hamiltonian of an abstract two-body dispersive system and the work is inspired by a recent result [3] which, under conditions including estimates of the mentioned type, opens up for spectral deformation and analytic perturbation theory of embedded eigenvalues of finite multiplicity.     

Numerical analysis of electronic conductivity in graphene with resonant adsorbates: comparison of monolayer and Bernal bilayer

We describe the electronic conductivity, as a function of the Fermi energy, in the Bernal bilayer graphene (BLG) in presence of a random distribution of vacancies that simulate resonant adsorbates. We compare it to monolayer (MLG) with the same defect concentrations. These transport properties are related to the values of fundamental length scales such as the elastic mean free path L _e , the localization length ξ and the inelastic mean free path L _i . Usually the later, which reflect the effect of inelastic scattering by phonons, strongly depends on temperature T. In BLG an additional characteristic distance l ₁ exists which is the typical traveling distance between two interlayer hopping events. We find that when the concentration of defects is smaller than 1%–2%, one has l ₁ ≤ L _e ? ξ and the BLG has transport properties that differ from those of the MLG independently of L _i (T). Whereas for larger concentration of defects L _e <l ₁ ? ξ, and depending on L _i (T), the transport in the BLG can be equivalent (or not) to that of two decoupled MLG. We compare two tight-binding model Hamiltonians with and without hopping beyond the nearest neighbors.     

Boson peak in various random-matrix models

A so-called boson peak in the reduced density g(ω)ω² of vibrational states is one of the most universal properties of amorphous solids (glasses). It quantifies the excess density of states above the Debye value at low frequencies ω. Its nature is not fully understood and, at a first sight, is nonuniversal. It is shown in this work that, under rather general assumptions, the boson peak emerges in a natural way in very dissimilar models of stable random dynamic matrices possessing translational symmetry. This peak can be shifted toward both higher and lower frequencies (down to zero frequency) by varying the parameters of the distribution and the degree of disorder in the system. The frequency ω_b of the boson peak appears to be proportional to the elastic modulus E of the system in all cases under investigation.     

Microwave photoresistance of a double quantum well at high filling factors

The effect of millimeter wave radiation on the electronic transport in a GaAs double quantum well at a temperature of 4.2 K in a magnetic field of up to 2 T has been studied. Resistance (conductance) oscillations have been shown to appear in the two-dimensional electronic system under investigation at high filling factors. The magnetic field positions of the oscillation maxima are determined by the condition Δ_SAS/? = lω_c, where Δ_SAS = (E ₂ ? E ₁) is the size quantization sublevel splitting in the quantum well, ω_c is the cyclotron frequency, and l is a positive integer. It has been found that the microwave field substantially modifies the oscillations in the double quantum well, which results in alternating two-frequency oscillations of photoresistance with the inverse magnetic field.     

The real solution to scalar field equation in 5D black string space

After the nontrivial quantum parameters Ω _n and quantum potentials V _n obtained in our previous research, the circumstance of a real scalar wave in the bulk is studied with the similar method of Brevik and Simonsen (Gen. Rel. Grav. 33:1839, 2001). The equation of a massless scalar field is solved numerically under the boundary conditions near the inner horizon r _e and the outer horizon r _c . Unlike the usual wave function Ψ_ωl in 4D, quantum number n introduces a new functions Ψ_{ωl n} , whose potentials are higher and wider with bigger n. Using the tangent approximation, a full boundary value problem about the Schrödinger-like equation is solved. With a convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients are obtained. If extra dimension does exist and is visible at the neighborhood of black holes, the unique wave function Ψ_{ωl n} may say something to it.     

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 ).     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

Spin susceptibility of cuprates in the model of a 2D frustrated antiferromagnet: Role of renormalization of spin fluctuations in describing neutron experiments

Experimental data on the spin susceptibility of HTSC cuprates are reproduced on the basis of a spherically symmetric approach in the frustrated Heisenberg model. The inclusion of real and imaginary renormalizations in spin Green’s functions makes it possible to explain the evolution of spin excitation spectrum ω(q) and susceptibility spectrum χ(q, ω) in the range from insulator to optimal doping. In the low-frustration limit corresponding to the weakly doped mode, the saddle singularity of ω(q) and scaling of χ_2D(ω) =∫d q Im χ(q, ω) are reproduced and an analytic expression is derived for the scaling function. In the strong frustration (optimal doping) mode, the stripe scenario is demonstrated; this leads to a peak of χ_2D (ω) in the region of ω～60 meV.     

Ab initio calculation of the lifetime of quasiparticle excitations in transition metals within the framework of the <Emphasis Type="Italic">GW</Emphasis> approximation

This paper reports on the results of ab initio calculations of the lifetimes τ of quasiparticle excitations in cubic d transition metals (V, Nb, Ta, Mo, W, Rh, Ir) within the GW approximation, which represents the self-energy of quasiparticles by the product of the Green’s function and the dynamically screened Coulomb potential. A comparative analysis of the dependences of the lifetime τ(ω) on the excitation energy ω is performed, and the specific features of the dependences τ(ω) in going from metal to metal within a particular group and along the d periods are revealed. It is found that the dependence τ(ω) on the excitation energy differs from the dependence τ ～ ω^?2 obtained within the free-electron model and is primarily determined by the density of d states localized in the vicinity of the Fermi level and by the electron interaction screened by the d electrons.