Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

On the pairing theory of the bose superfluid

W. A. B. EVANS, Y. Imry

Published Sep 1, 1969• 68 citations

DOI: 10.1007/bf02711051

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A original microscopic theory of superfluidity and superconductivity driven by the single particle (SPC) and pair condensation (PC) of attracting bosons both in Fermi and in Bose systems is developed. This theory (as distinct from the existing theories) for Fermi systems contains two order parameters Δ F and Δ B characterizing the attracting fermion pairs and boson pairs, respectively. In such systems superconducting (SC) phase transition is accompanied, as a rule, by the formation of k-space composite bosons (e.g. Cooper pairs and bipolarons) with their subsequent transition to the superfluid (SF) state by attractive SPC and PC. A novel Fermi-liquid and SF Bose-liquid theories are elaborated for description this two-stage Fermi–Bose-liquid (FBL) scenario of SC (or SF) transition. The crossover from k- to real (r)-space pairing regime for BCS-like coupling constants γ F ≃ 0.7-0.9 and the irrelevance of r-space pairs to the superconductivity are shown. The developed SF Bose-liquid theory predicts the first-order phase transition SPC ↔ PC of attracting 3d-bosons with the kink-like behaviors of all SC (SF) parameters near [Formula: see text] in accordance with the observations in 4 He , 3 He and superconductors. It is argued that the coexistence of the order parameters Δ F and Δ B leads to the superconductivity by two FBL scenarios. One of these scenarios is realized in the so-called fermion (type I, II and III) superconductors (FSC) (where formation of k-space composite bosons and their condensation occur at the same temperature) and the other in the boson (type II and III) superconductors (BSC) (where BCS-like pairing take place in the normal state with manifesting of the second-order phase transition and opening of the pseudogap at T=T F > T c ). There the gapless superfluidity (superconductivity) is caused by the gapless excitation spectrum of bosons at [Formula: see text] and not by the presence of point or line nodes of the BCS-like gap Δ F assumed in some s-, p- and d-pairing models. The 3D- and 2D-insulator–metal–superconductor phase diagrams are presented. The necessary and sufficient microscopic criterions for superfluidity is formulated. The theory proposed are in close agreement with the observations in 4 He , 3 He , superconductors, nuclear and neutron star matter, cosmology, etc.

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Various BCS-like pairing theories are still invariably used to describe the unusual superconducting/superfluid states and properties of condensed matters without clarifying the fermionic or bosonic nature of Cooper pairs and the relevant mechanisms of superconductivity and superfluidity. We show that the bosonization of Cooper pairs and the novel superconductivity and superfluidity resulting from the condensation of an attractive Bose gas of Cooper pairs into a superfluid state in high-Tc cuprates and other exotic systems occur under the condition εF≲2εA (where εF is the Fermi energy, εA is the energy of the effective attraction between fermions). We argue that the simple BCS criterion (i.e. formation of an energy gap on the Fermi surface) is insufficient for the occurrence of unconventional superconductivity (superfluidity) and the superconducting/superfluid transition in attractive Bose systems is more λ-like than the usual Bose–Einstein condensation. The new and specific criteria for unconventional superconductivity and superfluidity are formulated. Mean-field theory of the three- and two-dimensional superfluid Bose condensates of Cooper pairs describes reasonably well the novel superconducting states (i.e., two distinct superconducting phases below the bulk superconducting transition temperature Tc and a vortex-like state above Tc) and properties (such as λ-like transition at Tc, first-order phase transition and gapless bosonic excitations somewhat below Tc or even far below Tc) of high-Tc cuprates in full agreement with the experimental findings. The unusual superconducting/superfluid states and properties of heavy-fermion and organic compounds, Sr2RuO4, 3He, 4He and atomic Fermi gases are explained more clearly by this theory.

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