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Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and

Superconductivity and Superfluidity Unfortunately, no direct experiments of the effect of isotopic substitution on the electronic properties (such as the electronic specific heat and the Fermi energy), exist for metals substantial for our consideration. Let us consider what should be expected in such measurements. A convenient choice for the superconductor is mercury, as it has many isotopes and their isotope effect has been carefully measured back in the 50s of the last century as aforementioned. The linear dependence of the critical temperature of a superconductor on its Fermi energy (Eq.(6.20)) and also the existence of the isotope effect suggests the dependence of the ion density in the crystal lattice from the mass of the isotope. Let us consider what should be expected in such measurements. Even then, it was found that the isotope effect is described by Eq.(10.4) in only a few superconductors. In others, it displays different values, and therefore in a general case it can be described by introducing of the parameter a: Mi a T c = Const. (10.5) At taking into account Eq.(6.20), we can write T c ∼ E F ∼ n 2/3 e (10.6) The parameter l which characterizes the ion lattice obtains an increment ∆l with an isotope substitution: where M i and ∆M i are the mass of isotope and its increment. ∆l l = − a 2 · ∆M i M i , (10.7) It is generally accepted that in an accordance with the terms of the phonon mechanism, the parameter a ≈ 1 2 for mercury. However, the analysis of experimental data [35]-[36] (see Figure 4.3) shows that this parameter is actually closer to 1/3. Accordingly, one can expect that the ratio of the mercury parameters is close to: ) ( ( ∆l l ∆M i M i ) ≈ − 1 6 . (10.8) 106 Science Publishing Group

Chapter 11 Superfluidity as a Subsequence of Ordering of Zero-Point Oscillations 11.1 Zero-Point Oscillations of the Atoms and Superfluidity The main features of superfluidity of liquid helium became clear few decades ago [26], [27]. L. D. Landau explains this phenomenon as the manifestation of a quantum behavior of the macroscopic object. However, the causes and mechanism of the formation of superfluidity are not clear till our days. There is no explanation why the λ-transition in helium-4 occurs at about 2 K, that is about twice less than its boiling point: T boiling T λ ≈ 1.94, (11.1) while for helium-3, this transition is observed only at temperatures about a thousand times smaller.

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