We propose a two-dimensional (2D) band structure calculation for alcalineearth-substituted La2Cu04 in the tetragonal phase. We find a degenerate logarithmic singularity in the electronic density of states, as usual in 2D systems. This leads to an orthorhombic-to-tetragonal structural phase transition (SPT). Using the BCS theory, we calculate the superconducting critical temperature T, as a function of the position of the Fermi level (i.e. Cu+++/Cu++ ratio). This model explains the high T:s observed experimentally and the relation between superconductivity and SPT.

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Dans V3Si les atomes de vanadium sont disposés suivant des chaînes linéaires denses et on peut appliquer aux électrons d l'approximation des liaisons fortes à une dimension. On constate que l'énergie électronique ainsi calculée s'abaisse par déformation de la maille. Ceci peut constituer une explication, par un effet Jahn-Teller de bandes, du changement de phase cubique → tétragonale observé à basse température

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