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Fishman, R.S.

Princeton Univ., NJ (USA)

Princeton Univ., NJ (USA)

AbstractAbstract

[en] This thesis studies the magnetic response of

^{3}He on two energy scales: the Fermi energy epsilon/sub F/ in the normal state and the binding energy of Cooper pairs 2Δ in the superfluid. In the normal state it was found that the coupling between zero sound and longitudinal spin oscillations is proportional to γH/epsilon/sub F/, which is of order 10^{-3}for a 10 kG field. The superfluid is much more sensitive to a magnetic field because the S/sub z/ = +/-1 and S/sub z/ = 0 Cooper pair populations shift when γH becomes comparable to Δ approx. = 10^{-3}epsilon/sub F/. While depleting the S/sub z/ = 0 Cooper pair population, the magnetic field compresses the I = 1 gap and generates a I = 3 gap. These effects contribute to the enhancement of the magnetic susceptibility and to the nonlinear field splitting and dispersion of the real squashing modes. The dipole interaction distorts the B phase gap even in the absence of a magnetic field. To determine the Fermi liquid and pairing interactions that parametrize the quasi-particle vertex, these results are compared with the susceptibility data of Hoyt et al and the real squashing mode data of Shivaram et alSecondary Subject

Source

1985; 154 p; University Microfilms Order No. 85-29,772; Thesis (Ph. D.).

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Report

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Thesis/Dissertation

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AbstractAbstract

[en] In this paper a 1/z expansion is used to study the coupling of phase fluctuations in an array of superconducting grains. By lowering T

_{c}and increasing the critical grain diameter α_{c}, fluctuations suppress the long-range order in the material. When the temperature T is of order U = e^{2}/C, where C is the grain capacitance, peaks appear in the fluctuation corrections to both the specific heat and the short-range order parameter. These peaks are induced by the coupling between thermal fluctuations of the charge and quantum fluctuations of the phase on neighboring grainsSecondary Subject

Source

Cody, G.D.; Sheng, P. (Exxon Corporate Research Lab., Annandale, NJ (United States)); Geballe, T.H. (Stanford Univ., Stanford, CA (United States)); 677 p; ISBN 1-55899-084-4; ; 1990; p. 363-368; Materials Research Society; Pittsburgh, PA (United States); Spring meeting of the Materials Research Society (MRS); San Francisco, CA (United States); 16-21 Apr 1990; CONF-900466--; Materials Research Society, 9800 McKnight Rd., Suite 327, Pittsburgh, PA 15237 (USA)

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Book

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Conference

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AbstractAbstract

[en] The force-balance method is used to calculate the isothermal resistivity to first order in the electric field. To lowest order in the impurity potential, the isothermal resistivity disagrees with the adiabatic results of the Kubo formula and the Boltzmann equation. However, an expansion of the isothermal resistivity in powers of the impurity potential is divergent, with two sets of divergent terms. The first set arises from the density matrix of the relative electron-phonon system. The second set arises from the explicit dependence of the density matrix on the electric field, which was ignored by force-balance calculations. These divergent contributions are calculated inductively, by applying a recursion relation for the Green's functions. Using the λ

^{2}t→∞ limit of van Hove, I show that the resummation of these divergent terms yields the same result for the resistivity as the adiabatic calculations, in direct analogy with the work of Argyres and Sigel, and Huberman and ChesterRecord Type

Journal Article

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[en] Quasiparticle dissipation in a granular superconductor is modeled by an effective nearest-neighbor capacitance ΔC between the grains of a superconducting array. Using an expansion in 1/z, where z is the number of nearest neighbors in the array, I study the effects of quasiparticle dissipation on the transition temperature and short-range order of a granular superconductor. In agreement with experimental results, quasiparticle dissipation suppresses the quantum fluctuations in a superconducting array. If the self-capacitance of a grain is C

_{0}, then both the long-range and the short-range order of the array are enhanced as the ratio λ=C_{0}/zΔC decreases. In disagreement with other work, the transition temperature is not reentrant for any value of λ. The results of this formalism, which consistently treats quantum fluctuations to first order in 1/z, should be valid in three-dimensional materialsRecord Type

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[en] The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid

^{3}He-B are calculated perturbatively in (γH/Δ) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (γHapprox.0.10Δ), there are low-field (γHapprox.q^{2}v/sub f/^{2}/Δ) nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of^{3}He-B depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactionsRecord Type

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[en] We consider a Josephson-coupled superconducting array with finite quantum fluctuations, arising from a nonzero capacitive charging energy, placed in a transverse magnetic field. To estimate the superconducting transition temperature as a function of magnetic field, we introduce a Hartree-type mean-field approximation. With no applied magnetic field, this approximation is very similar to that of Simanek, but unlike the latter, it does not lead to a reentrant normal phase transition. Reentrance is absent because we include no 4π-periodic eigenstates of Mathieu's equation in calculating quantum-statistical expectation values. We argue that these 4π-periodic functions are properly omitted because the original Hamiltonian does not include pair-breaking terms. With charging energies included, we find the transition temperature to be highly nonmonotonic in magnetic field, just as in the zero-capacitance limit. For every field B, there exists an upper critical charging energy U/sub c/(B) above which the array is normal even at T = 0; this charging energy is highly nonmonotonic in field. A brief comparison is made between our results and other recent calculations involving superconducting arrays in the presence of charging energies

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[en] In this paper we treat the effect of Coulomb interactions between the grains of a Josephson-junction array or a granular superconductor, in the presence of a magnetic field. By using the duality transformation developed by Chui and Weeks, we are able to study both the low-T/sub c/ and the high self-capacitance limits for d-dimensional cubic arrays. We examine two models for the Coulomb interaction matrix U. In the first, only the diagonal and nearest-neighbor interactions are nonzero. In the other, only the diagonal and nearest-neighbor components of the capacitance matrix C = U/sup -1/ are nonzero. Our results for the nearest-neighbor U/sub i//sub j/ model agree with the results of Fazekas, who found no sign of normal state reentrance in two or three dimensions. In the second model, reentrance occurs when the dimensionless parameter λ, related to the inverse screening length of the Coulomb interactions, becomes smaller than a critical value λ/sup */. For both models, the off-diagonal interactions enhance the transition temperature by reducing the cost of Cooper-pair tunneling. We compare the results of the second model with experimental observations of charging effects and reentrance in three dimensions

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[en] This paper uses the self-consistent phase-phonon approximation to study the effect of long-range Coulomb interactions in a superconducting array. We find that crucial features of the results of mean-field theory are confirmed: long-range interactions enhance the superconducting state and lower the critical value of the grain diameter, below which superconductivity is impossible. However, the reentrant phase transition found in the mean-field solution is absent from the self-consistent results. This may be because the self-consistent approximation is invalid when the superconducting state is suppressed and phase fluctuations are large, such as in the reentrant regime of the mean-field theory

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[en] Spin diffusion within the double-exchange model is studied in the limits W<< T<< J

_{H}S (intermediate temperatures) and W<< J_{H}S<< T (infinite temperature), where W is the electron bandwidth, T is the temperature, S is the local spin, and J_{H}is the Hund's coupling. In both limits, T is still far above the Curie temperature T_{C}∼W. All dynamical properties are obtained from the spin-current correlation function C(x), where x denotes time. While C(x) is real (even) at infinite temperature, it contains both real (even) and imaginary (odd) parts at intermediate temperatures. Upper and lower Tchebycheff bounds are used to evaluate the real part of C(x) in each limit. From C(ω), we construct the spin conductivity D(ω), which has Gaussian peaks at ω=0 and ± 2J_{H}S, all with the same width ∼W. Whereas the central peak is produced by the hopping of electrons between sites, the side peaks are produced by the mutual precession of the local and itinerant spins at every site. At infinite temperature, each of the side peaks has half the weight of the central peak. But at intermediate temperatures, the side peaks are reduced by T/(J_{H}S)<<1 as the spin precession becomes energetically prohibitive. A rigorous f-sum rule relates the integral over D(ω) to the average kinetic energy at any temperature. In the zero-frequency limit, the spin-diffusion coefficient D_{s}=(1/2)D(ω=0) yields the relaxation time τ_{r}(k)=1/(D_{s}k^{2}) for a magnetic disturbance with wavevector k. Whereas D_{s}reaches a maximum at half-filling (an average of one electron per site) for infinite temperature, it vanishes at half-filling for intermediate temperatures because an electron cannot hop to a neighbouring site without sacrificing enormous Hund's energy. The predictions of this work are compared with recent neutron-scattering measurements on the manganites. (author)Source

Available online at the Web site for the Journal of Physics. Condensed Matter (ISSN 1361-6448X) http://www.iop.org/; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. Condensed Matter; ISSN 0953-8984; ; v. 14(6); p. 1337-1352

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[en] The trial free energy of the harmonic approximation, which has been widely used to study Josephson junctions, diverges to negative infinity in the normal state for any finite temperature because a nonperiodic, harmonic Hamiltonian is used to describe a periodic system. In this paper, I employ a periodic, scalloped potential to construct a well-defined free energy, which is then minimized to obtain self-consistent solutions that are close to the harmonic solutions when phase fluctuations are small

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