Small objects in superfluid <sup>3</sup>He

Rainer, D.; Vuorio, Marja

doi:10.1088/0022-3719/10/16/018

Cited by 98 publications

(51 citation statements)

References 11 publications

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“…The transport cross section is reasonably approximated in the normal state by the geometric cross section err 2, and from the Einstein relation we find Op2/kBT = 3~2/p20"tr ~ 3.n'/(pvR) 2 (17) Typically pFR = 10 and thus Dp 2/kB T ~ 0.1. The constancy of the resulting mobility e/tz ~-n3pF~R 2, agrees well with experiment down to To.…”

Section: Equation For the Mobilitymentioning

confidence: 59%

Mobility of negative ions in superfluid 3He-B

1979

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We calculate the mobility of negative ions in superfluid 3He-B. We first derive the general formula for the mobility, and show that to a good approximation the scattering of quasiparticles from an ion may be treated as elastic, both in the superfluid for temperatures not too far below the transition temperature and also in the normal state. The scattering cross section in the superfluid is then calculated in terms of normal state properties; as we show, it is vital to include the effects of superfluid correlations on intermediate states in the scattering process. We find that for quasiparticles near the gap edge, the quasiparticle-ion scattering amplitude has a resonant behavior, and that as a result of interference among many partial waves, the differential scattering cross section is strongly peaked in the forward direction and reduced at larger angles, in much the same way as in diffraction. The transport cross section for such a quasiparticle is strongly reduced compared to that for a normal state quasiparticle, and the mobility is consequently strongly enhanced. Detailed calculations of the mobility which contain essentially no free parameters, agree well with the experimental data.

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Section: Equation For the Mobilitymentioning

confidence: 59%

Mobility of negative ions in superfluid 3He-B

1979

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“…This was analyzed quasiclassically by Choi and Muzikar (1989a), based on an earlier work of Rainer and Vuorio (1977), who considered the inhuence of small scattering centers on superfluid He [another treatment of the problem was offered by Mineev (1989)]. We shall here consider the Ginzburg-Landau approach to this problem, which is only valid in the region of a slow variation of the order parameter.…”

Section: The Magnetic Effect Of Impurities or Lattice Defectsmentioning

confidence: 99%

“…The classical correlation function then leads to the following additional contribution to the homogeneous kernel in Eq. (4.11) (see Rainer and Vuorio, 1977): where do(r, r')/dQ is the differential cross section [o(r)= f dQ'der(r, r')/dQ]. This formula contains both the scattering (first cross-section term) and the shadow scattering (second cross-section term).…”

Section: The Magnetic Effect Of Impurities or Lattice Defectsmentioning

confidence: 99%

Phenomenological theory of unconventional superconductivity

1991

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This article is a review of recent developments in the phenomenological description of unconventional superconductivity.Starting with the BCS theory of superconductivity with anisotropic Cooper pairing, the authors explain the group-theoretical derivation of the generalized Ginzburg-Landau theory for unconventional superconductivity. This is used to classify the possible superconducting states in a system with given crystal symmetry, including strong-coupling effects and spin-orbit interaction. On the basis of the BCS theory the unusual low-temperature properties and the (resonant) impurity scattering effects are discussed for superconductors with anisotropic pairing. Using the Ginzburg-Landau theory, the authors study several bulk properties of such superconductors: spontaneous lattice distortion, upper critical magnetic field, splitting of a phase transition due to uniaxial stress. Two possible mechanisms for ultrasound absorption are discussed: collective modes and damping by domain-wall motion. The boundary conditions for the Ginzburg-Landau theory are derived from a correlation function formulation and by grouptheoretical methods. They are applied to a study of the Josephson and proximity effects if unconventional superconductors are involved there. The magnetic properties of superconductors that break time-reversal symmetry are analyzed. Examples of current and magnetic-field distributions close to inhomogeneities of the superconducting order parameter are given and their physical origin is discussed. Vortices in a superconductor with a multicomponent order parameter can exhibit various topo1ogical structures. As examples the authors show fractional vortices on domain walls and nonaxial vortices in the bulk. Furthermore, the problem of the possible coexistence of a superconducting and a magnetically ordered phase in an unconventional superconductor is analyzed. The combination of two order parameters that are almost degenerate in their critical temperature is considered with respect to the phase-transition behavior and effects on the lower and upper critical fields. Because heavy-fermion superconductors -which are possible realizations of unconventional superconductivity -have been the main motivation for the phenomenological studies presented here, the authors compare the theoretical results with the experimental facts and data. In particular, they emphasize the intriguing features of the compound UPt3 and consider in detail the alloy U& Th Be/3.

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“…Moreover, since for a given value of the maximum gap A the A-phase gap is smaller, on the average, than in the B phase, one finds that both/Zlf and tz• are less than/ZB, the B-phase ion mobility at the same value of A/T. In order to compare the constant-cross-section calculation with experiment, let us evaluate the mobility increase in the superfluid near Tc using (23) and (24). Within weak coupling theory one has AZ(T) = 5 2 ~ABcs(T), where A(T) is the maximum gap in the ABM state.…”

Section: Ion Mobility Tensormentioning

confidence: 99%

Mobility tensor of negative ions in superfluid 3He-A

1980

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The mobility tensor of negative ions in the A phase of superfluid 3He is calculated for temperatures close to To. In this regime the scattering of superfluid quasiparticles from an electron bubble is practically elastic and the mobility tensor is expressed in terms of momentum transfer cross sections for an ion at rest. These generalized transport cross sections are obtained from the quasiparticle-ion scattering T-matrix, which we evaluate in terms of the normal state scattering amplitude. The p-wave pairing correlations in the intermediate states result in important interference effects among all partial waves in the scattering process, and, in addition, for the low-energy quasiparticles they lead to resonant states below the gap edge. These phenomena modify the scattering amplitude in the superfluid in an essential way and the differential quasiparticle-ion cross section is found to display strongly anisotropic, energy-dependent variations on the scale of the superfluid energy gap. We find that, in contrast to simple approximations, for low quasiparticle energies the parallel and perpendicular momentum transfer cross sections are very different from one another. Close to To, the calculated mobility remains rather isotropic, but at lower temperatures the anisotropy is considerably larger than predicted by simple approximations for the cross section. The computed results are compared with the available measurements.

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Small objects in superfluid ³He

Abstract: Distortions in the superfluid order parameter around a small object in 3He are calculated, together with the supercurrents and the angular momentum induced by it in the liquid. The forces acting on the impurity due to the liquid texture structure are also considered.

Cited by 98 publications

References 11 publications

Mobility of negative ions in superfluid 3He-B

Mobility of negative ions in superfluid 3He-B

Phenomenological theory of unconventional superconductivity

Mobility tensor of negative ions in superfluid 3He-A

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Small objects in superfluid 3He

Abstract: Distortions in the superfluid order parameter around a small object in 3He are calculated, together with the supercurrents and the angular momentum induced by it in the liquid. The forces acting on the impurity due to the liquid texture structure are also considered.

Cited by 98 publications

References 11 publications

Mobility of negative ions in superfluid 3He-B

Mobility of negative ions in superfluid 3He-B

Phenomenological theory of unconventional superconductivity

Mobility tensor of negative ions in superfluid 3He-A

Contact Info

Product

Resources

About

Small objects in superfluid ³He