Comment on "`Inconsistency of the conventional theory of superconductivity"' by Hirsch J.E
Jacob Szeftel, Nicolas Sandeau, Michel Abou Ghantous, Antoine Khater
aa r X i v : . [ phy s i c s . g e n - ph ] J u l epl draft Comment on "‘Inconsistency of the conventional theory of super-conductivity"’ by Hirsch J.E.
Jacob Szeftel , Nicolas Sandeau , Michel Abou Ghantous and Antoine Khater ENS Cachan, LPQM, 61 avenue du Président Wilson, 94230 Cachan, France Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, F-13013 Marseille, France American University of Technology, AUT Halat, Highway, Lebanon Université du Maine, UMR 6087 Laboratoire PEC, F-72000 Le Mans France
PACS nn.mm.xx – 74.20-z
PACS nn.mm.xx – 74.25.Bt
Abstract –A rebuttal of arXiv : 1909 . An Incorrect Assumption. –
Hirsch’s rationale [1]relies on an assumption, dating back to London’s interpre-tation [3] of the Meissner effect, that the thermodynamicalstate, characterising a superconductor of type I, submittedto a time-dependent magnetic field H ( t ), reaching eventu-ally a constant value H ( t f ) for t ≥ t f , would depend only on final temperature T ( t f ) and field H ( t f ) but would beconversely independent from the transient regime ( t < t f ),characterised by dHdt ( t < t f ) = 0 and (or) dTdt ( t < t f ) = 0.As shown elsewhere [2, 4], such a claim, which entails fur-thermore that the skin-depth is independent from the fre-quency ω and equal to λ L / √ λ L being London’slength [5], would be indeed true [2], if the electrical con-ductivity of the material were infinite. However, sincethe ac conductivity was later measured to be finite , albeitmuch larger than the normal one, it was ascribed solely tonormal electrons [5], while the superconducting ones werestill believed to have infinite conductivity.Unfortunately, this mainstream view has been disproved[6], by showing on the basis of low-frequency susceptibilitydata [7–10], that the skin-depth was not equal to λ L / √ / √ ω for ω →
0, as seen innormal metals, and the conductivity, if ascribed to nor-mal electrons, should be lower than the normal one, incontradiction with experiment. In conclusion, contraryto a long-standing fallacy, the final ( t ≥ t f ) state in theMeissner effect does indeed depend [6] on the whole tran-sient ( t < t f ) regime, due to irreversible consequences of finite ac conductivity. Since Hirsch’s main argument [1]has been thereby rebutted, we could end our review at thatpoint. But it is worth pursuing this subject, because themuddled discussion [1] of the Meissner and Joule effectsneed clarification. Meissner effect. –
Although Hirsch [1] has long fa-vored an interpretation of the Meissner effect, based on quantum pressure [11], he suddenly embraces quite anunrelated explanation [2, 4, 6]. In this novel view, theMeissner effect is ascribed to the susceptibility χ , goingfrom paramagnetic ( χ n >
0) in the normal (
T > T c )state to diamagnetic ( χ s <
0) in the superconducting(
T < T c ) one ( T c stands for the critical temperature).Despite H remaining constant allover the cooling process,the magnetic induction B is indeed altered at T c becauseof χ s − χ n = 0 ⇒ dBdt = 0, which gives rise, owing to theFaraday-Maxwell equation, to eddy currents flowing at theouter edge of the sample and screening H . Besides, dueto the finite conductivity in the superconducting state [2],there is λ M >> λ L with λ M being the penetration depthof H .Hirsch tries to apply [1] this argument for T < T c byascribing dχdt = 0 to dλ L dT = 0 during the transient regime dTdt ( t < t f ) = 0. However, such a claim runs afoul [2] at χ ( T < T c ) ∝ (cid:16) λ L λ M (cid:17) , which could only depend upon T via the relaxation time [12] of the electron kinetic energy, τ . Nevertheless, τ is very likely to be T independent atp-1acob Szeftel1 Nicolas Sandeau2 Michel Abou Ghantous3 Antoine Khater4such low temperature, for which it is limited by residualimpurities. Joule effect. –
Hirsch ascribes [1] the whole Jouleheat released during the transient regime to eddy currents,carried by normal electrons. However their contribution isnegligible because the ac conductivity of superconductingelectrons can be larger than the normal one by 5 five ordersof magnitude [9], which has been confirmed by analysingsusceptibility data [6].The thermal balance, supposed to account [1] for T ( t REFERENCES[1] Hirsch J.E. , arXiv : 1909.12786.[2] Szeftel J. and Sandeau N. and Khater A. , Prog.In.Electro.Res.M , (2018) 69.[3] London F. , Superfluids , Vol. (Wiley) 1950.[4] Szeftel J. and Sandeau N. and Khater A. , Phys.Lett.A , (2017) 1525.[5] Tinkham M. , Introduction to Superconductivity (DoverBooks) 2004.[6] Szeftel J. and Abou Ghantous M. and Sandeau N. , Prog.In.Electro.Res.M , (2019) 1.[7] Maxwell E. and Strongin M. , Phys.Rev.Lett. , (1963) 10.[8] Strongin M. and Maxwell E. , Phys.Lett. , (1963)6.[9] Geshkenbein V.B. et al. , Phys. Rev.B , (1991) 3748.[10] Samarappuli S. et al. , Physica C , (1992) 159.[11] Hirsch J.E. , J.Supercond.Nov.Mag. , (2010) 309.[12] Ashcroft N.W. and Mermin N. D. , Solid StatePhysics (Saunders College) 1976.[13] Landau L.D. and Lifshitz E.M. , Statistical Physics (Pergamon Press, London) 1959.[14] Szeftel J. and Sandeau N. and Abou Ghantous M. , Eur.Phys.J.B , (2019) 67.[15] Szeftel J. and Sandeau N. and Abou Ghantous M. , J.Supercond.Nov.Mag. , (2020) 1307.(2020) 1307.