On the admissible values of the static magnetic permeability

Dolgov, O. V.; Kirzhnit︠s︡, D. A.; Losyakov, V. V.

doi:10.1016/0038-1098(83)90597-5

Cited by 11 publications

(17 citation statements)

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“…In the static case the additional free energy in the presence of an externally controlled current distribution j ext ͑k͒ (we use a transversal gauge) can be written in the form [8]:…”

mentioning

confidence: 99%

TDependence of the Magnetic Penetration Depth in Unconventional Superconductors at Low Temperatures: Can It Be Linear?

Schopohl

Dolgov

1998

Phys. Rev. Lett.

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We present a thermodynamics argument against a strictly linear temperature dependence of the magnetic penetration depth, which applies to superconductors with arbitrary pairing symmetry at low temperatures. [S0031-9007(98) PACS numbers: 74.25.Nf, 74.20.Fg, 74.72.Bk Some evidence for an unconventional d x 2 2y 2 -pairing symmetry in cuprate high-T c superconductors is provided by recent angle resolved photoemission experiments [1]. A striking proof for the d x 2 2y 2 symmetry of the Cooper pairs in cuprates arises from the observation of a spontaneously generated half flux quantum in Josephson tunneling experiments carried out on tetracrystal substrates [2]. Early support for the possibility of a d x 2 2y 2 symmetry of the Cooper pairs in cuprate high-T c superconductors came from the observation of a linear T dependence of the magnetic penetration depth [3,4] at low temperatures T : l͑T͒ 2 l͑0͒~T .(1) Such a linear T dependence of the magnetic penetration depth (MPD) has a topological origin. If the order parameter associated with the Cooper pair condensate vanishes along node lines on the Fermi surface the spectrum N s ͑E͒ of quasiparticle excitations in the superconducting phase is gapless and varies proportional to E at low excitation energies: N s ͑E͒~E for E ø D max . For this reason a pure d x 2 2y 2 -pairing state (node lines along k x 6k y ) should display a strictly linear dependence of MPD vs T at low temperatures. In previous work this effect was also discussed for the polar phase in a triplet pairing superconductor, e.g., [5].New experiments [6] indicate deviations from this linearity of MPD with temperature, for example, a T 2 dependence of MPD below some crossover temperature T ‫ء‬ was measured. Such a behavior may occur due to various reasons. For example, Kosztin and Leggett [7] explain this behavior in terms of nonlocal electrodynamics. Their argument is, that in clean d x 2 2y 2 -pairing superconductors there exist surface induced nonlocal effects, which lead to a T 2 dependence of l ab ͑T͒ 2 l ab ͑0͒, as extracted from optical and microwave experiments with the magnetic field orientated parallel to the b c direction. On the other hand, in experiments with the magnetic field orientated perpendicular to the b c direction the T dependence of MPD cannot be altered by the Kosztin-Leggett effect.Since the Kosztin-Leggett effect [7] really depends on the existence of a surface in the problem it cannot be applied to other measurement techniques of MPD, for example, direct static magnetic measurements, measurements of vortex properties, the lower critical magnetic field B c1 , muon spin relaxation. Such techniques of measuring MPD have bulk character.In the following, we present a proof (based on linear response theory), for arbitrary superconductors, that a strictly linear T dependence of MPD at low temperatures violates the third law of thermodynamics. For simplicity, let us consider a uniform system where all properties depend on coordinates r 2 r 0 only. The current-current correlator,

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“…In the static case the additional free energy in the presence of an externally controlled current distribution j ext ͑k͒ (we use a transversal gauge) can be written in the form [8]:…”

mentioning

confidence: 99%

TDependence of the Magnetic Penetration Depth in Unconventional Superconductors at Low Temperatures: Can It Be Linear?

Schopohl

Dolgov

1998

Phys. Rev. Lett.

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“…also follow directly from (2.4), see [14,15] We are interested here in taking into account not only the sum rules, but other exact relations as well. We wish to consider multi-species systems and the method of moments does not involve essentially the local-field corrections and expresses the dynamic properties in terms of the system static characteristics like the static structure factors and the moments themselves.…”

Section: The Loss Functionmentioning

confidence: 99%

The loss function of dense plasmas and sum rules

Arkhipov¹,

Ashikbayeva²,

Askaruly³

et al. 2014

INT J MATH PHYS

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Abstract. Mathematical, particularly, asymptotic properties of the RPA and RPA with dynamic local field corrections of the coupled plasma dielectric function are analyzed within the method of moments which satisfies some exact relations. Particularly f-sum rule,higher-order sum rules and other conservation laws. Thehigher-order sum rules take into account the correlations in the system under scrutiny, so if the system dynamic characteristics, e.g., the dielectric function, do not satisfy these rules which are effectively additional conservation laws, it is difficult to expect the corresponding model to be adequate in the strong-coupling domain.Some other drawbacks and advantages of the above models are pointed out.

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“…[29]. However, we next show how negative-μ media can be effectively emulated by replacing them with a set of currents.…”

Section: Emulating Negative-permeability Materialsmentioning

confidence: 99%

“…One of these is the possibility of having negative-μ materials; whereas resonances in different kinds of natural and artifical substances can yield negative values of μ and ε at nonzero frequencies [24][25][26][27][28], no such negative-μ materials exist in magnetostatics [29]. Negative values of μ and ε have enabled very interesting novel phenomena for electromagnetic waves, like perfect lenses [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

“…The theory is confirmed by experimentally constructing a spherical shell that emulates a negative-permeability material in a uniform magnetic field. In this way, the effective properties of three-dimensional (3D) negative-μ materials can be produced in practice, overcoming the fact that passive materials with negative permeability do no exist in magnetostatics [29].…”

Section: Introductionmentioning

confidence: 99%

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Negative permeability in magnetostatics and its experimental demonstration

et al. 2017

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The control of magnetic fields, essential for our science and technology, is currently achieved by magnetic materials with positive permeability, including ferromagnetic, paramagnetic, and diamagnetic types. Here we introduce materials with negative static permeability as a new paradigm for manipulating magnetic fields. As a first step, we extend the solutions of Maxwell magnetostatic equations to include negative-permeability values. The understanding of these new solutions allow us to devise a negative-permeability material as a suitably tailored set of currents arranged in space, overcoming the fact that passive materials with negative permeability do no exist in magnetostatics. We confirm the theory by experimentally creating a spherical shell that emulates a negative-permeability material in a uniform magnetic field. Our results open new possibilities for creating and manipulating magnetic fields, which can be useful for practical applications.

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On the admissible values of the static magnetic permeability

Cited by 11 publications

References 1 publication

TDependence of the Magnetic Penetration Depth in Unconventional Superconductors at Low Temperatures: Can It Be Linear?

TDependence of the Magnetic Penetration Depth in Unconventional Superconductors at Low Temperatures: Can It Be Linear?

The loss function of dense plasmas and sum rules

Negative permeability in magnetostatics and its experimental demonstration

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