Author

# G. Rickayzen

Bio: G. Rickayzen is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Superconductivity & Meissner effect. The author has an hindex of 4, co-authored 4 publications receiving 473 citations.

##### Papers

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TL;DR: In this article, a theory of the thermal conductivity of superconductors is presented, based on the theory of super conductivity due to Bardeen, Cooper, and Schrieffer, which is treated as quasi-particles, allowing a Boltzmann equation to be set up.

Abstract: A theory of the thermal conductivity of superconductors is presented, based on the theory of superconductivity due to Bardeen, Cooper, and Schrieffer. The excited states of the system are treated as quasi-particles, allowing a Boltzmann equation to be set up. The electronic contribution to the thermal conductivity when the dominant scatterers are impurities has been calculated exactly. The result is very close to that of the Heisenberg-Koppe theory which is in fair agreement with experiment. The variational principle of Wilson has been used to find the electronic conductivity when the dominant scatterers are lattice waves. It is concluded that the theory fails to predict the sharp drop in the ratio $\frac{{\ensuremath{\kappa}}_{\mathrm{es}}}{{\ensuremath{\kappa}}_{\mathrm{en}}}$ as the temperature is lowered below ${T}_{c}$, a feature which is characteristic of the experimental results. The effect of the electrons on the lattice conductivity has also been calculated. The theoretical values may be too large.

362 citations

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TL;DR: In this paper, the complex dielectric constant of a superconductor and the Meissner effect are derived in a manner which is gauge invariant, from the theory of superconductivity due to Bardeen, Cooper, and Schrieffer.

Abstract: The complex dielectric constant of a superconductor and the Meissner effect are derived in a manner which is gauge invariant, from the theory of superconductivity due to Bardeen, Cooper, and Schrieffer. The collective excitations are important in maintaining gauge invariance; the longitudinal collective excitations ensure that a static vector potential produces no longitudinal current and the transverse collective excitations contribute to the Meissner current an amount which depends on the angular properties of the two-body interaction. This contribution is estimated to be small. An earlier calculation of ultrasonic absorption in superconductors is justified. The whole investigation is based upon the generalized random-phase approximation introduced by Anderson and applies whether or not the Coulomb interaction between the electrons is taken into account. The equations of motion are linearized in such a way that the exchange terms are automatically screened if the Coulomb interaction is, in fact, taken into account. The region of applicability of most of the results is limited by the approximations to temperatures at or near absolute zero.

78 citations

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TL;DR: In this article, it was shown from a manifestly gauge-invariant Hamiltonian that the Meissner effect can follow from an energy-gap model of superconductivity.

Abstract: It is shown from a manifestly gauge-invariant Hamiltonian that the Meissner effect can follow from an energy-gap model of superconductivity. The superconductor is described by Fr\"ohlich's Hamiltonian and the superconducting properties at the absolute zero are determined by a method due to Bogoliubov. In the weak-coupling limit (${T}_{c}\ensuremath{\ll}{\ensuremath{\Theta}}_{D}$) there is an energy gap which leads to a Meissner effect. The method of Bogoliubov is extended to apply at general temperatures and the current is calculated in the weak-coupling limit. The results are in essential agreement with those of Bardeen, Cooper, and Schrieffer.

31 citations

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TL;DR: In this article, it was shown that the solution they obtained by a variational method is correct to $O(1/n)$ for a large system and the single particle Green's function is derived and used to calculate the interaction energy.

Abstract: In their theory of superconductivity, Bardeen, Cooper, and Schrieffer made use of a reduced Hamiltonian which included only scattering of pairs of particles of opposite momentum and spin. It is shown that the solution they obtained by a variational method is correct to $O(\frac{1}{n})$ for a large system. The single particle Green's function is derived and used to calculate the interaction energy.

22 citations

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TL;DR: In this paper, a superconductive solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian, and the pions of finite mass are found as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangians which otherwise possesses a certain type of the ∆-ensuremath{gamma{5}$ invariance.

Abstract: Continuing the program developed in a previous paper, a "superconductive" solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian. We find the pions of finite mass as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangian which otherwise possesses a certain type of the ${\ensuremath{\gamma}}_{5}$ invariance. In addition, heavier mesons and two-nucleon bound states are obtained in the same approximation. On the basis of numerical mass relations, it is suggested that the bare nucleon field is similar to the electron-neutrino field, and further speculations are made concerning the complete description of the baryons and leptons.

3,923 citations

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TL;DR: In this paper, the spin transport in a nonmagnetic metal connected to ferromagnetic injector and detector electrodes was studied and a general expression for the spin accumulation signal which covers from the metallic to the tunneling regime was derived.

Abstract: We study theoretically the spin transport in a nonmagnetic metal connected to ferromagnetic injector and detector electrodes. We derive a general expression for the spin accumulation signal which covers from the metallic to the tunneling regime. This enables us to discuss recent controversy on spin injection and detection experiments. Extending the result to a superconducting device, we find that the spin accumulation signal is strongly enhanced by opening of the superconducting gap since a gapped superconductor is a low carrier system for spin transport but not for charge. The enhancement is also expected in semiconductor devices.

444 citations

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TL;DR: In this article, a review of the physical and technical constraints that influence single-electron charge transport is presented, and a broad variety of proposed realizations are presented, some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently "just" wild ideas, still often potentially competitive if technical constraints can be lifted.

Abstract: The control electrons at the level of the elementary charge e was demonstrated experimentally already in the 1980s. Ever since, the production of an electrical current ef, or its integer multiple, at a drive frequency f has been in a focus of research for metrological purposes.This review discusses the generic physical phenomena and technical constraints that influence single-electron charge transport and presents a broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently ‘‘just’’ wild ideas, still often potentially competitive if technical constraints can be lifted. The important issues of readout of singleelectron events and potential error correction schemes based on them are also discussed. Finally, an account is given of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and applications and uses of single-electron devices outside the metrological context are briefly discussed.

330 citations

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TL;DR: In this article, the authors derived a set of linearized equations for the deviation from the equilibrium value of the quasiparticle distribution function as well as of the order parameter, and the equations were solved for the case of an injection of a stationary quaiparticle into a superconductor.

Abstract: Starting from the equation of Gor'kov and Eliashberg in a form introduced by Eilenberger, we derive a set of linearized equations for the deviation from the equilibrium value of the quasiparticle distribution function as well as of the order parameter. These equations resemble the Boltzmann equation and the Ginzburg-Landau equation, respectively, and they form a set of coupled equations. Two different modes can be distinguished, depending on whether the order parameter changes in magnitude or in phase. The equations are solved for the case of a stationary quasiparticle injection into a superconductor and the change in the electrochemical potential of the quasiparticles is calculated. Furthermore, we treat the problem of a current flowing perpendicular to a superconducting-normal interface in which a normal current is converted into a supercurrent, and we calculate the extra resistance of the interface.

280 citations

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TL;DR: In this article, the behavior of quasi-particles in Bi 2 Sr 2 CaCu 2 O 8 in a magnetic field was probed by measurement of the thermal conductivity κ.

Abstract: Quasi-particles (QPs) are excitations of the superconducting state. The behavior of QPs in Bi 2 Sr 2 CaCu 2 O 8 in a magnetic field was probed by measurement of the thermal conductivity κ. An anomaly in κ was observed at low temperatures. At a transition field H k , κ displayed a sharp break in slope, followed by a plateau region in which it ceased to change with increasing field. The nonanalytic nature of the break at H k suggests a phase transition of the condensate to a state in which the QP current is zero (the system remains superconducting). Detailed measurements of the new regime are presented, and implications for the QPs and the superconducting state are discussed.

185 citations