The model of a hypothetical room-temperature superconductor

Grigorishin, Konstantin V.; Lev, B. I.

doi:10.48550/arxiv.1408.6761

2014

DOI: 10.48550/arxiv.1408.6761

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The model of a hypothetical room-temperature superconductor

Konstantin V. Grigorishin¹,

B. I. Lev²

Abstract: The model of hypothetical superconductivity, where the energy gap asymptotically approaches zero as temperature increases, has been proposed. Formally the critical temperature of such a superconductor is equal to infinity. For practical realization of the hypothesis a superconducting material with such properties is predicted.

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2015

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“…This model does not solve the problem of room-temperature superconductivity, however it allows to reformulate the problem. Possible practical realization of the model is proposed in [8], where a source of the external pair potential has been constructed.…”

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confidence: 99%

Toy model of superconductivity

Grigorishin

Lev

2015

Low Temperature Physics

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The model of hypothetical superconductivity, where the energy gap asymptotically approaches zero as temperature or magnetic field increases, has been proposed. Formally the critical temperature and the second critical field for such a superconductor is equal to infinity. Thus the material is in superconducting state always. PACS numbers: 74.20.Fg, 74.20.Mn Critical temperature T C and critical magnetic fields H c , H c2 are most important characteristics of a superconductor. The critical parameters depends on an effective coupling constant with some collective excitations g = ν F λ 1 (here ν F is a density of states at Fermi level, λ is an interaction constant), on frequency of the collective excitations ω and on correlation length ξ 0 . The larger coupling constant, the larger these critical parameters. For example, for large values of g we have T C ∝ ω √ g [1, 2] (or T C ∝ ωg in BCS theory). Formally the critical temperature can be made arbitrarily large by increasing the electron-phonon coupling constant. However in order to reach room temperature such values of the coupling constant are necessary which are not possible in real materials. Moreover we can increase the frequency ω due nonphonon pairing mechanisms as proposed in [2]. However with increasing of the frequency the coupling constant decreases as g ∝ 1/ω, therefore T C (ω → ∞) = 1.14ω exp (−1/g) → 0. The second critical magnetic field can be enlarge due to the decrease of the correlation length in "dirty limit, where l is a free length. However the critical field is low near the critical temperature: H c2 (T → T C ) → 0. In a present work we generalize BCS model so that the problem of the critical parameters is removed due to the fact that a ratio between the gap and the critical temperature (2∆/T C = 3 ÷ 7 for presently known materials) is changed to 2∆/T C → 0. We consider a system of fermions with Hamiltonian:where H BCS is BCS Hamiltonian -kinetic energy + pairing interaction ( which are the complex order parameter ∆ = |∆|e iθ . The multipliers ∆ |∆| and ∆ + |∆| are introduced into H ext in order that the energy does not depend on the phase θ (a → ae iθ/2 , a

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confidence: 99%

Toy model of superconductivity

Grigorishin

Lev

2015

Low Temperature Physics

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The model of a hypothetical room-temperature superconductor

Cited by 1 publication

References 20 publications

Toy model of superconductivity

Toy model of superconductivity

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