Dependence of the magnitude and direction of the persistent current on the magnetic flux in superconducting rings

The obtained periodic magnetic-field dependences I _c+(Φ/Φ₀) and I _c?(Φ/Φ₀) of the critical current measured in opposite directions on asymmetric superconducting aluminum rings has made it possible to explain previously observed quantum oscillations of dc voltage as a result of alternating current rectification. It was found that a higher rectification efficiency of both single rings and ring systems is caused by hysteresis of the current-voltage characteristics. The asymmetry of current-voltage characteristics providing the rectification effect is due to the relative shifts of the magnetic dependences I _c?(Φ/Φ₀) = I _c+(Φ/Φ₀ + Δ?) of the critical current measured in opposite directions. This shift means that the position of I _c+(Φ/Φ₀) and I _c?(Φ/Φ₀) minima does not correspond to n + 0.5 magnetic flux Φ quanta, which is in direct contradiction to measured Little-Parks resistance oscillations. Despite this contradiction, the amplitude I _{c, an}(Φ/Φ₀) = I _c+(Φ/Φ₀) ? I _c?(Φ/Φ₀) of critical current anisotropy oscillations and its variations with temperature correspond to the expected amplitude of persistent current oscillations and its variations with temperature.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Spin-precession-induced currents through ferromagnet/nanomagnet/superconductor junctions

The spin-precession-induced current through ferromagnet/nanomagnet/superconductorjunctions is investigated by using the nonequilibrium Green’s function method. It is foundthat the charge current I _c for the spinprecession frequency ω less than the energy gap Δ onlyarises from the equal-spin Andreev reflection, which is independent of the spinpolarization p of the ferromagnetic lead, while that forω > Δ mainly originates from the quasiparticle’scontribution. Both equal-spin AR and quasiparticle scattering processes contribute to thespin current I _s and the quasiparticlescattering process plays a dominant role. WhileI _c forω < Δ can be enhanced by the spin polarizationp, I _s decreases withp. These features may be of interest for ongoing experiments in thefield of molecular spintronics.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. II. Distributions with Heavy Tails

We study the asymptotic structure of the first K largest eigenvalues λ _k,V and the corresponding eigenfunctions ψ(?;λ _k,V ) of a finite-volume Anderson model (discrete Schrödinger operator) \(\mathcal{H}_{V}= \kappa \Delta_{V}+\xi(\cdot)\) on the multidimensional lattice torus V increasing to the whole of lattice ? ^ν , provided the distribution function F(?) of i.i.d. potential ξ(?) satisfies condition ?log(1?F(t))=o(t ³) and some additional regularity conditions as t→∞. For z∈V, denote by λ ⁰(z) the principal eigenvalue of the “single-peak” Hamiltonian κΔ _V +ξ(z)δ _z in l ²(V), and let \(\lambda^{0}_{k,V}\) be the kth largest value of the sample λ ⁰(?) in V. We first show that the eigenvalues λ _k,V are asymptotically close to \(\lambda^{0}_{k,V}\). We then prove extremal type limit theorems (i.e., Poisson statistics) for the normalized eigenvalues (λ _k,V ?B _V )a _V , where the normalizing constants a _V >0 and B _V are chosen the same as in the corresponding limit theorems for \(\lambda^{0}_{k,V}\). The eigenfunction ψ(?;λ _k,V ) is shown to be asymptotically completely localized (as V↑?) at the sites z _k,V ∈V defined by \(\lambda^{0}(z_{k,V})=\lambda^{0}_{k,V}\). Proofs are based on the finite-rank (in particular, rank one) perturbation arguments for discrete Schrödinger operator when potential peaks are sparse.     

Nonlinear electric and thermoelectric Andreev transport through a hybrid quantum dot coupled to ferromagnetic and superconducting leads

We discuss the nonlinear Andreev current of an interacting quantum dot coupled to spin-polarized and superconducting reservoirs when voltage and temperature biases are applied across the nanostructure. Due to the particle-hole symmetry introduced by the superconducting (S) lead, the subgap spin current vanishes identically. Nevertheless, the Andreev charge current depends on the degree of polarization in the ferromagnetic (F) contact since the shift of electrostatic internal potential of the conductor depends on spin orientation of the charge carrier. This spin-dependent potential shift characterizes nonlinear responses in our device. We show how the subgap current versus the bias voltage or temperature difference depends on the lead polarization in two cases, namely (i) S-dominant case, when the dot-superconductor tunneling rate (Γ _R ) is much higher than the ferromagnet-dot tunnel coupling (Γ _L ), and (ii) F-dominant case, when Γ _L ? Γ _R . For the ferromagnetic dominant case the spin-dependent potential shows a nonmonotonic behavior as the dot level is detuned. Thus the subgap current can also exhibit interesting behaviors such as current rectification and the maximization of thermocurrents with smaller thermal biases when the lead polarization and the quantum dot level are adjusted.     

The Andreev conductance in superconductor–insulator–normal metal structures

The Andreev subgap conductance at 0.08–0.2 K in thin-film superconductor (aluminum)–insulator–normal metal (copper, hafnium, or aluminum with iron-sublayer-suppressed superconductivity) structures is studied. The measurements are performed in a magnetic field oriented either along the normal or in the plane of the structure. The dc current–voltage (I–U) characteristics of samples are described using a sum of the Andreev subgap current dominating in the absence of the field at bias voltages U < (0.2–0.4)Δ_c/e (where Δ_c is the energy gap of the superconductor) and the single-carrier tunneling current that predominates at large voltages. To within the measurement accuracy of 1–2%, the Andreev current corresponds to the formula \({I_n} + {I_s} = {K_n}\tanh \left( {{{eU} \mathord{\left/ {\vphantom {{eU} {2k{T_{eff}}}}} \right. \kern-\nulldelimiterspace} {2k{T_{eff}}}}} \right) + {K_s}{{\left( {{{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} \right)} {\sqrt {1 - {{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - {{eU} \mathord{\left/ {\vphantom {{eU} {{\Delta _c}}}} \right. \kern-\nulldelimiterspace} {{\Delta _c}}}} }}\) following from a theory that takes into account mesoscopic phenomena with properly selected effective temperature T _eff and the temperature- and fieldindependent parameters K _n and K _s (characterizing the diffusion of electrons in the normal metal and superconductor, respectively). The experimental value of K _n agrees in order of magnitude with the theoretical prediction, while K _s is several dozen times larger than the theoretical value. The values of T _eff in the absence of the field for the structures with copper and hafnium are close to the sample temperature, while the value for aluminum with an iron sublayer is several times greater than this temperature. For the structure with copper at T = 0.08–0.1 K in the magnetic field B_|| = 200–300 G oriented in the plane of the sample, the effective temperature T _eff increases to 0.4 K, while that in the perpendicular (normal) field B _⊥ ≈ 30 G increases to 0.17 K. In large fields, the Andreev conductance cannot be reliably recognized against the background of single- carrier tunneling current. In the structures with hafnium and in those with aluminum on an iron sublayer, the influence of the magnetic field is not observed.     

Nonlinear Hall effect in a quasi-two-dimensional electron system

The nonlinear electron transport in GaAs double quantum wells with two occupied size-quantization levels has been studied at a temperature of 4.2 K in the magnetic fields B < 1 T. It has been found that a sinusoidal electric current I _ac induces the generation of higher harmonics of both longitudinal V _xx (B) and Hall V _xy (B) voltages in the quasi-two-dimensional electron system under consideration. The Hall voltage oscillating in the magnetic field has been shown to appear in the electron system with two occupied size-quantization levels in the presence of microwave radiation and dc electric current I _dc. The experimental data indicate the independent contributions of the diagonal and off-diagonal components of the conductivity tensor to the nonlinear magnetotransport at high filling factors.     

Zur Chronologie des alten Ägypten

The velocityv of the propagation of discharge along the anode of a self-quenchingG—M-counter is a function of total pressureP, pressure of the quenching gasP _D, radius of the cathoder _a and of the anoder _i andV _ü the difference between working- and starting-potential. For the mixtures argon-methylal, argon-alcohol and helium-alcohol isv=v ₀·exp[k·(V _ü/V _e)^1/2] withv ₀ the velocity at the starting potentialV _e v ₀=(a+b·P _D/P)·V _n ^1/2 ·exp [(c?d·P_D/P·V _n ^?1/2 ] andV _n=V _e·(lnr _a/r _i)^?1.k, a, b, c andd are characteristical constants of the filling gas.     

Maslov index for power-law potentials

The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = ?V ₀/x ^s, x > 0, 0 < s < 2 The result for the potential V(x)=-V ₀/x ^1/2 is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.     

Ion-pair states of I<Subscript>2</Subscript>, Br<Subscript>2</Subscript>, IBr,and ICl

The experimentally determined energies and rotational constants of the vibrational levels v = 0–20 of the Ion-Pair states Ω = 0⁺, Ω = 1 of the I₂, Br₂, IBr, and ICl molecules are modeled. The model used includes three diabatic states, which correlate to X⁺(3P, 1D) + Y^～(1S₀). These states are coupled by the spin-orbit interaction, which is assumed to be independent of the internuclear distance. For IBr and ICl, as well as for the ungerade states of I₂ and Br₂, satisfactory results are obtained. The model is less applicable to the gerade states of I₂ and Br₂, which is possibly results from the retainment of the asymptotic J _A J _B coupling of the angular momenta at equilibrium internuclear distances.     

Growth of (GaAs)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(ZnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solution films and investigation of their structural and some photoelectric properties

Single-crystal films of the substitutional solid solution (GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) on GaAs substrates have been grown using liquid phase epitaxy. The X-ray diffraction patterns, photoluminescence spectra, and current-voltage characteristics of the n-(GaAs)-p-(GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) heterostructures prepared have been investigated. The lattice parameters of the film a _f = 5.6544 Å and the substrate a _s = 5.6465 Å have been determined, and the profile of the molecular distribution of the solid solution components has been obtained. The photoluminescence spectrum of the (GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) films exhibits a narrow peak (against the background of the broad luminescence band) with a maximum in the luminescence intensity at a photon energy of 2.67 eV due to the presence of Zn-Se bonds in the structure (ZnSe is covalently bonded to the tetrahedral lattice of the GaAs matrix). It has been shown that the direct branch of the current-voltage characteristics of the structures under investigation is described by an exponential dependence I = I ₀exp(qV/ckT) at low voltages (V > 0.3 V) and by a power-law dependence I ～ V ^α with exponents α = 4 at V = 0.4–0.8 V, α = 2 at V = 0.8–1.4 V, and α = 1.5 at V > 2 V. The experimental results have been explained in the framework of the double-injection model for the n-p-p ⁺ structure under the condition that the concentration distribution of nonequilibrium charge carriers has a minimum.     

Analytical model of a Brownian motor with a fluctuating potential

We propose a model of a Brownian motor that performs a useful work against a load force F in an asymmetric periodic potential V(x) = V(x + 2L) that undergoes random shifts by a half period L with a frequency γ. An arbitrarily shaped potential profile is repeated with an energy shift ΔV in both half-periods L, while the periodicity of the function V(x) is ensured by its jumps at x = 0 and x = L. The boundary condition at x = 0 for the distribution function of a Brownian particle allows us to introduce a high and narrow potential barrier V₀ that blocks the reverse current and leads to high efficiency of the motor (the ratio of the useful work done against the load force F to the energy imparted to the particle through the potential shifts). Based on this model, we derived exact analytical expressions for the current J and the efficiency η. In the special case of piecewise-linear potentials, J and η were plotted against F and γ for various values of the parameters ΔV and V₀. We discuss the influence of the potential shape and fluctuation frequency on the main characteristics of the motor.     

Magnetoresistance hysteresis in granular HTSCs as a manifestation of the magnetic flux trapped by superconducting grains in YBCO + CuO composites

Hysterestic behavior of the magnetoresistance of granular HTSCs and its interaction with the magnetic hysteresis are studied by measuring magnetoresistance R(H) and critical current I _c(H) of composites formed by HTSC Y_0.75Lu_0.25Ba₂Cu₃O₇ and CuO. A network of Josephson junctions is formed in such composites, in which the nonsuperconducting component plays the role of barriers between HTSC grains. Hysteretic dependences R(H) of magnetoresistance are studied in a wide range of transport current density j and are analyzed in the framework of the two-level model of a granular superconductor, in which dissipation takes place in the Josephson medium and the magnetic flux can be pinned both in grains and in the Josephson medium. The interrelation between the hysteresis of critical current I _c(H) and the evolution of the hysterestic dependence R(H) of the magnetoresistance upon transport current variation is demonstrated experimentally. The effect of the magnetic past history on the hysteretic behavior of R(H) and the emergence of a segment with a negative magnetoresistance are analyzed. It is shown for the first time that the R(H) dependences are characterized by a parameter that is independent of the transport current, viz., the width of the R(H) hysteresis loop.     

Inverse Scattering at Fixed Energy on Surfaces with Euclidean Ends

On a fixed Riemann surface (M ₀, g ₀) with N Euclidean ends and genus g, we show that, under a topological condition, the scattering matrix S _V (λ) at frequency λ > 0 for the operator Δ+V determines the potential V if \({V\in C^{1,\alpha}(M_0)\cap e^{-\gamma d(\cdot,z_0)^j}L^\infty(M_0)}\) for all γ > 0 and for some \({j\in\{1,2\}}\) , where d(z, z ₀) denotes the distance from z to a fixed point \({z_0\in M_0}\) . The topological condition is given by \({N\geq \max(2g+1,2)}\) for j = 1 and by N ≥ g + 1 if j = 2. In \({\mathbb {R}^2}\) this implies that the operator S _V (λ) determines any C ^{1, α} potential V such that \({V(z)=O(e^{-\gamma|z|^2})}\) for all γ > 0.     

Penetration of a magnetic field into the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript> high-temperature superconductor: Magnetoresistance in weak magnetic fields

The penetration of a magnetic field into superconducting grains and weak links of YBa₂Cu₃O_7?δ ceramic high-temperature superconductors is investigated using measurements of the transverse and longitudinal magnetoresistances at T=77.3 K and 0≤H≤～500 Oe as a function of the transport current in the range ～0.01≤I/I _c ≤～0.99. The effects associated with the complete penetration of Josephson vortices into weak links of the high-temperature superconductor in magnetic fields H_c2J, the onset of penetration of Abrikosov vortices into superconducting grains in magnetic fields H_c1A, and the first-order transition from the Bragg glass phase to the vortex glass phase in fields H_BG-VG are revealed and interpreted. The I-H phase diagrams YBa₂Cu₃O_7?δ high-temperature superconductors are constructed for I ⊥ H and I ‖ H.     

Percolation and the electron–electron interaction in an array of antidots

A square lattice of microcontacts with a period of 1 μm in a dense low-mobility two-dimensional electron gas is studied experimentally and numerically. At the variation of the gate voltage V _g , the conductivity of the array varies by five orders of magnitude in the temperature range T from 1.4 to 77 K in good agreement with the formula σ(V _g ) = (V _g ?V _g ^* (T))^β with β = 4. The saturation of σ(T) at low temperatures is absent because of the electron–electron interaction. A random-lattice model with a phenomenological potential in microcontacts reproduces the dependence σ(T, V _g ) and makes it possible to determine the fraction of microcontacts x(V _g , T) with conductances higher than σ. It is found that the dependence x(V _g ) is nonlinear and the critical exponent in the formula σ ∝ ? (x - 1/2) ^t in the range 1.3 < t(T, V _g ) < β.     

Scattering the Geometry of Weighted Graphs

Given two weighted graphs (X, b_k, m_k), k =?1,2 with b₁ ～ b₂ and m₁ ～ m₂, we prove a weighted L¹-criterion for the existence and completeness of the wave operators W_±(H₂, H₁, I_1,2), where H_k denotes the natural Laplacian in ?²(X, m_k) w.r.t. (X, b_k, m_k) and I_1,2 the trivial identification of ?²(X, m₁) with ?²(X, m₂). In particular, this entails a general criterion for the absolutely continuous spectra of H₁ and H₂ to be equal.     

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.     

Das Kernquadrupolmoment des Mn55

With a recording photoelectric Fabry-Perot spectrometer and an atomic-beam light source the hyperfine structure of the Mn I-resonance linesλ=4031 Å,λ=4033 Å,λ=4034 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁶ P _7/2,5/2,3/2 ⁰)and of the inter-combination linesλ=5395 Å andλ=5433 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁸ P _7/2,5/2 ⁰) was measured. Furthermore the resonance lines have been measured with a pulsed atomic-beam in absorption. In this case the quotient (I ₀(ν)?I(ν))/I ₀(ν) was recorded, whereI(ν)=I ₀(ν) exp(?α(ν)d) is the observed intensity with absorption andI ₀(ν) the intensity of the light source. From the hyperfine structure splitting the value of the electric quadrupole moment of Mn⁵⁵ was derived to be:Q(Mn⁵⁵)=+(0.35±0.05)·10^?24 cm².