Discrepancy between theory and measurement of superconducting vanadium

Zheng, X. H.; Walmsley, D.G.

doi:10.1016/j.physc.2015.05.007

Cited by 7 publications

(10 citation statements)

References 38 publications

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“…Superconductivity then arises solely from residual umklapp scattering of pairs (in real crystalline systems normal and umklapp scattering always coexist and the exclusively normal scattering scenario does not arise). In a series of publications we proved the validity of this empirical rule: it allows consistent potentials for the electron-phonon interaction to be used to evaluate both normal state electrical resistivity and superconducting tunnelling conductance with high accuracy in lead, aluminium, niobium and tantalum [3,4] as well as in tungsten, iridium, molybdenum and vanadium [19,20].…”

Section: Historical Backgroundmentioning

confidence: 91%

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BCS theory has to be overhauled: Reassurance from numerical survival rate

Zheng¹,

Walmsley²

2016

Solid State Communications

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The BCS theory has conceptual and numerical difficulties. We have previously overhauled it with a new scheme of phonon-mediated electron pairing that can be expressed analytically in terms of an empirical pairing survival rate factor, S(q) = 0 or 1/2, depending on phonon momentum, q. Now we evaluate S(q) numerically entirely from experimental data on normal state electrical resistivity and on superconducting tunnelling conductance. The empirical and numerical S(q) are reassuringly close in aluminium and lead and particularly so in two other cases, niobium and tantalum.

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Section: Historical Backgroundmentioning

confidence: 91%

“…Now the numerical value of T c is reduced when reasonable values of ρ(T ) are implemented. It turns out that the introduction of the empirical S(q) settles the BCS numerical issue in the cases of lead, aluminium, niobium and tantalum with high accuracy [3,4] as it does too in tungsten, iridium, molybdenum and vanadium [19,20].…”

Section: Introductionmentioning

confidence: 99%

BCS theory has to be overhauled: Reassurance from numerical survival rate

Zheng¹,

Walmsley²

2016

Solid State Communications

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“…In a series of publications we established the worth of Eq. (4) in that it allows the same pseudopotential to be used to evaluate the electron-phonon interaction for both normal state resistivity and superconductivity with high accuracy [9,10,12,13]. Indeed it becomes clear that the new pairing potential is much better in that it is close to the resistivity-derived potential and contrasts with the BCS potential.…”

Section: Bcs Difficultymentioning

confidence: 99%

“…2). Extensive tests demonstrate that the numerical difficulty of the BCS theory also is remedied to high accuracy when this consideration is taken into account [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Visualised predictions of gap anisotropy to test new electron pairing scheme

Zheng

Walmsley

2017

Physica C: Superconductivity and its Applications

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The rich and fertile but not yet adequately exploited ground of superconductor anisotropy is proposed as a test bed for a new empirical scheme of electron pairing. The scheme is directed to resolving a numerical and conceptual difficulty in the BCS theory. The original theoretical formulation of the anisotropy problem by Bennett is adopted and its outcomes extensively explored. Here the Bennett conclusion that in metallic superconductors phonon anisotropy is the principal source of gap anisotropy is accepted. Values of the energy gap are visualised globally in k-space with unprecedented detail and accuracy. Comparison is made between the anisotropy pattern from the new and the usual BCS pairing schemes. Differences are revealed for future experimental resolution.

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“…Also, the attention is drawn to the fact that even significant modification of the pairing interaction, responsible for the creation of the superconducting state, does not cause a significant decline in the value of the Coulomb pseudopotential. For example, taking into account the modified pairing mechanism of the BCS theory [32] and the X-ray scattering data from synchrotron and vacuum tube sources allows to obtain following estimation: μ = 0.279 (bright X-rays) and μ = 0.298 (weak X-rays).…”

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confidence: 99%

Characteristics of Superconducting State in Vanadium: the Eliashberg Equations and Semi-analytical Formulas

Drzazga

Domagalska

Jarosik

et al. 2017

J Supercond Nov Magn

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The superconducting state in vanadium characterizes with the critical temperature (T c ) equal to 5.3 K. The Coulomb pseudopotential, calculated with the help of the Eliashberg equations, possesses anomalously high value μ (3 max ) = 0.259 or μ (10 max ) = 0.368 ( max denotes the maximum phonon frequency). Despite the relatively large electron-phonon coupling constant (λ = 0.91), the quantities such as the order parameter ( ), the specific heat (C), and the thermodynamic critical field (H c ) determine the values of the dimensionless ratios not deviating much from the predictions of the BCS theory: R = Keywords Electron-phonon superconductivity in vanadium · Eliashberg theory · Semi-analytical approach · Coulomb pseudopotential · Thermodynamic propertiesThe classical Eliashberg theory is used to quantitative description of the superconducting state, which is mediated by the electron-phonon interaction [1]. The strong-coupling and the retardation effects omitted in BCS model [2,3] are included in the Eliashberg theory by assumption that the electron band energy is directly renormalized by the frequency-dependent order parameter ( n = (iω n )), the wave function renormalization factor (Z n = Z (iω n )), and the energy shift function (χ n = χ (iω n )). The symbol ω n = (π/β) (2n − 1) denotes the Matsubara frequency, β = 1/ k B T , where k B is the Boltzmann constant. In most cases, the materials, in which we observe the phonon induced superconducting state, characterize with the very wide electron band (W max , where W denotes the half-width of the band, and max is the Debye frequency). For this reason, the analysis of the superconducting state can be conducted with the help of the Eliashberg equations for the half-filled electron band [4,5]:whereas the order parameter is given by the formula n = φ n /Z n . The electron-phonon pairing kernel has the form of λ (iω n − iω m ) = 2 +∞ 0 dω α 2 F (ω)ω (ω n −ω m ) 2 +ω 2 . The spectral function α 2 F (ω) is usually calculated numerically by using the ab initio approach, where the electron band energy, the

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Discrepancy between theory and measurement of superconducting vanadium

Cited by 7 publications

References 38 publications

BCS theory has to be overhauled: Reassurance from numerical survival rate

BCS theory has to be overhauled: Reassurance from numerical survival rate

Visualised predictions of gap anisotropy to test new electron pairing scheme

Characteristics of Superconducting State in Vanadium: the Eliashberg Equations and Semi-analytical Formulas

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