Definition of the Differential Reaction Rate in Ammonia Synthesis kinetics

Anderson, R. B.; Toor, H. L.

doi:10.1021/j150581a051

Cited by 56 publications

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“…From the symmetry and angular momentum, the chiral p-wave vortex core with L z = 0 can be identified with the s-wave superconductors in the absence of the magnetic field. For the latter, non-magnetic impurities are known to be harmless (the Anderson theorem 43) ). These two explain why non-magnetic impurities are harmless in the chiral p-wave vortex with L z = 0.…”

Section: Modification Due To Finite κmentioning

confidence: 99%

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Kato

Hayashi

2001

J. Phys. Soc. Jpn.

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The pair-potential and current density around a single vortex of the two-dimensional chiral p-wave superconductor with d = z (px ± ipy) are determined self-consistently within the quasiclassical theory of superconductivity. Shrinking of the vortex core at low temperatures are considered numerically and analytically. Temperature-dependences of the spatial variation of pair-potential and circular current around the core and density of states at zero energy are the same as those in the isotropic s-wave case. When the senses of vorticity and chirality are opposite, however, we find two novel results; 1) the scattering rate due to non-magnetic impurities is considerably suppressed, compared to that in the s-wave vortex. From this observation, we expect that the chiral p-wave superconductors provide the best chance to observe the shrinking of the vortex ("Kramer-Pesch effect") experimentally.2) The pair-potential of chiral p-wave superconductors inside vortex core recovers a combined time-reversal-Gauge symmetry, although this symmetry is broken in the region far from the vortex core. This local recovery of symmetry leads to the suppression of the impurity effect inside vortex core.KEYWORDS: Superconductivity, vortex, quasiclassical theory, Kramer-Pesch effect, chiral superconductors §1. IntroductionThe superconducting state in Sr 2 RuO 4 1) is expected to be unconventional; a Knight shift measurement in planar magnetic field suggests odd-parity pairing with d vector perpendicular to the RuO 2 plane.2) Muon spin relaxation experiment suggests spontaneous magnetization;3) this means that time-reversal symmetry is broken spontaneously in the superconducting state. The simplest pairing symmetry which is consistent with the above two experimental results and the tetragonal crystal symmetry is given by the odd-parity pairing with d =ẑ (p x ± ip y ).4) This is commonly called the "chiral p-wave superconducting state" because the Cooper pair has a definite angular momentum L z = ±1 in the internal motion. A singly quantized vortex is, on the other hand, a configuration of the pair-potential where the center-of-mass motion of Cooper pair has an angular momentum. The interplay between vorticity and chirality would bring about intriguing phenomena in vortex physics of Sr 2 RuO 4 . Indeed, several authors 5-8) have argued that the impurity effects in vortex core of chiral p-wave superconductor is considerably suppressed, compared to that in s-wave vortex core. The fact that the superclean regime is realized within the core of chiral pwave vortex has several implications. First, the flux flow conductivity is expected to be enhanced at low temperatures in the chiral p-wave vortex states.8) Second, a large Hall effect is also expected. Third, the shrinkage of vortex cores at low temperatures, which is referred to as "the Kramer-Pesch (KP) effect", 9) is free from the * E-mail: yusuke@phys.c.u-tokyo.ac.jp * * E-mail: hayashi@mp.okayama-u.ac.jp smearing due to impurities. The vortex shrinking effect in chiral p-wave superconductors i...

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Section: Modification Due To Finite κmentioning

confidence: 99%

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Kato

Hayashi

2001

J. Phys. Soc. Jpn.

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“…This effect, which is ascribed to the Anderson theorem [1], limits the influence of long-range phase coherence phenomena to situations in which lowenergy quasi-particles persist: notably, the physics of hybrid SN-compounds, and those which exhibit unconventional (e.g. d-wave) symmetry.…”

Section: Introductionmentioning

confidence: 99%

Tail states in disordered superconductors with magnetic impurities: the unitarity limit

Marchetti¹,

Simons²

2002

J. Phys. A: Math. Gen.

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When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that 'optimal fluctuations' of the random impurity potential can lead to the nucleation of 'domains' of localised states within the gap region predicted by the conventional Abrikosov-Gor'kov mean-field theory, rendering the superconducting system gapless at any finite impurity concentration. By implementing a field theoretic scheme tailored to the weakly disordered system, the aim of the present paper is to extend this analysis to the consideration of magnetic impurities in the unitarity scattering limit. This investigation reveals that the qualitative behaviour is maintained while the density of states exhibits a rich structure.

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“…The suppression of NMR coherence peak may be attributed to (a) gap anisotropy [5]/non s-wave pairing of superconducting phase [6,7], (b) strong coupling damping [8][9][10], (c) paramagnetic impurities in samples [5,11], and/or (d) strong Coulomb interaction such as paramagnon/antiparamagnon effects [12,13]. The non-magnetic impurity scatterings, on the other hand, have no influence on (T 1 T ) −1 [11,14,15], other than the smearing of gap anisotropy. This is because (a) there exists a simple scaling relation between the renormalization function of pure (Z(ω)) and impure ( Z(ω)) superconductors and (b) in the expression for (T 1 T ) −1 , the numerator and denominator are of the same powers in Z(ω), as will be discussed in more detail later.…”

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confidence: 99%

“…We need to carry out the summation over the Matsubara frequency ip and the momentum q in Eq. (15), and then take analytic continuation and the limit ω → 0 as given in Eq. (8).…”

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Effects of impurity vertex correction on the NMR coherence peak ins-wave superconductors

Choi

Mele²

1995

Phys. Rev. B

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We study the effects of non-magnetic impurity vertex correction on nuclear spin-lattice relaxation rate 1/T 1 of conventional s-wave superconductors within the Eliashberg formalism. We obtain, with a self-consistent t−matrix treatment of impurity scatterings, the expressions for impurity vertex function and nuclear spin-lattice relaxation rate. The 1/T 1 is evaluated with a simple approximation on angular average, and found to agree in clean limit with the previous result that 1/(T 1 T ) remains unrenormalized under the impurity vertex correction. As dirtiness is increased, on the other hand, the coherence peak in 1/(T 1 T ) is found to increase due to the impurity vertex correction.This result is discussed in connection with the experimental observations on conventional superconductors.

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Definition of the Differential Reaction Rate in Ammonia Synthesis kinetics

Cited by 56 publications

References 0 publications

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Kramer–Pesch Effect in Chiral p-Wave Superconductors

Tail states in disordered superconductors with magnetic impurities: the unitarity limit

Effects of impurity vertex correction on the NMR coherence peak ins-wave superconductors

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