Strong-Coupling Superconductivity inV3Xtype of Compounds

Abstract

Recent works 1 "" 5 have shown that the unusual physical properties of high superconducting A 3 B type of intermetallic compounds, such as V 3 Si and Nb 3 Sn, could be understood on the basis of a very fine d-band structure. The Fermi level Ey in the normal state should fall in a very narrow peak of the density of states n(E). This peak lies just above the bottom E m of a nearly empty d sub-band (Fig. 1). Detailed calculations show that the energy range EY~E m of occupied states in the peak is much smaller than the width HOOJJ of the phonon spectrum and of the order of the superconductive gap. For instance, in V 3 Si, EY~E m in the normal state should be equal to 18 xlO"" 4 eV ^22°K. The same situation seems to arise in Nb 3 Sn.In the usual BCS theory the energy-range limitation to the attractive interaction between two pairing electrons arises from the narrowness of the phonon spectrum. On the contrary, assuming here that the d electrons are the superconducting ones, 6 we may expect the energy-range limitation to be imposed by the narrowness of the electronic spectrum. So the exact value of Hoop would not influence the energy gap, in agreement with the extreme smallness of the observed isotopic effect in Nb 3 Sn. 7 Moreover, the very large density of states near the bottom of the d sub-band is related to a Bloch energy E(k) which varies slowly with the wave vector k. The variation with k of the kinetic energy £=£(&)-£jp of the Bloch states involved is small compared with the energy gap A. This fact brings such compounds near to the strong-coupling limit of superconductivity where all the electrons can be involved in Cooper pairs, owing to their nearly equal kinetic energy. If Q is the small number of d electrons present in the peak of Fig. 1, and if we neglect contributions from other bands, two equations must be solved in the BCS formalism 8 to obtain the gap A at absolute zero:V is the BCS coupling constant; w(f) is the density of states for one spin direction. It is given by 1 n(£)=B(£-£ )-1/2 , mwhere B is a normalization constant.For small Q, all the electrons involved are in the peak of n(f). Thus the upper limit in Eqs. (1) and (2), being large compared with the width of this peak, is not important (Fig. 1). We shall take it as infinite.By introducing the new variable x = A~1 /2 (£ ~£ m ) 1/2 , Eqs. (1) and (2) lead to Q = 2B 2 VIJ, A = B 2 V 2 J 2 with •n

Shell structure and strengthening of superconducting pair correlation in nanoclusters

“…If the HOS is highly degenerate , this means that this shell contains many electrons, which can be viewed as a sharp peak in the density of states at the Fermi level. Situation is similar to that studied in [31 ] for bulk materials; the presence of a peak in the density of states results in a noticeable increase in T C .…”

On the nature of antiferromagnetism in the CuO $ \mathsf {_2}$ planes of oxide superconductors

“…The divergence in δE is also somewhat larger than the contributions to n(E) along the side AB of the square, where, as in a one dimensional problem [27], they diverge as δE -1/2 . This striking result comes from the square geometry of the Fermi surface of non doped samples ; it is also found in the ionic limit, if one assumes also electrons to be delocalised.…”

BCS-Bose crossover theory extended with hole Cooper pairs

“…Note that the extended crossover predicts T c values for aforementioned SCs quite well, even for the so-called BCS theory "bad" actors. 22 Here, we solved two equations just as suggested by Keldysh et al, 3 Popov, 4 Friedel et al, 5 Eagles and finally Leggett, 7 rather than just one (the gap) equation with µ = E F as assumed in BCS theory.…”

“…A year later, Popov 4 suggested a theory of a Bose gas made up of bound pairs of Fermi particles which in the small density limit describes a system behaving as a Bose gas whose particles should form a Bose condensate at low enough temperatures. In 1967, Friedel et al 5 proposed that "two equations must be solved in the BCS formalism to obtain the gap equation at T = 0." A couple of years later, Eagles 6 studied two simultaneous equations for the BCS gap ∆ and its associated fermionic chemical potential µ.…”