Cooper Pairs in Alternating Lay - ers of Light and Heavy Atoms

The Hamiltonian and trial function in the BCS theory are improved to test the limit of this theory. The Cooper pairs arise from standing electron waves, ready to move with atoms, giving high T c. The Hamiltonian is derived from alternating layers of light and heavy atoms, giving a forbidden zone hosting no standing wave pairs. The exchange term may force singlet pairs into this zone, leaving triplet pairs outside, giving magnetic excitations. If the Fermi energy is crossed only by the CuO 2 band, then the forbidden zone and triplet pairs will vanish, consistent with experimental evidence. PACS: 74.20.Fg-BCS theory and its development PACS: 74.80.-g-Spatially inhomogeneous structures 1 Recently there has been considerable interest in the original theory of Bardeen, Cooper and Schriefer (BCS) [1]. It was used by Nunner, Schmalian and Bennemann to explain the isotopic effect of cuprates [2]. It was also used byNozì eres and Pistolesi to study pseudogaps [3]. Following this line of thinking, we adopt the view that cuprates have a Fermi surface and electron-phonon interactions. We also adopt the BCS formalism, which is relatively simple, due to neglecting damping and retardation, with negligible effects [4]. The BCS theory is based on variational evaluation of the Fröhlich Hamil-tonian, with the Cooper pairs as the trial function [1, 5]. With an improved Hamiltonian and trial function, we may explain further properties of cuprates. In order to improve the Hamiltonian, we use a simple model of alternating layers of light and heavy atoms (Fig. 1), because in cuprates the CuO 2 layers are always sandwiched by heavy atoms. For example, in La 2 CuO 4 we have a ratio 96/310 when comparing the atomic wt. of the CuO 2 layer and the two LaO layers. In YBa 2 Cu 3 O 7 we have a ratio 281/386 when comparing the two CuO 2 layers (including the Y atom in between) with other atoms. In Tl 2 Ba 2 CuO 6 the ratio is 96/746, which becomes 256/746 and 416/746 when the number of CuO 2 layers are 2 and 3 (including Ca in between). In HgBa 2 CuO 4 the ratios are 96/507, 232/507 and 368/507 when the number of CuO 2 planes are 1, 2 and 3 (including Ca in between) [6]. The classic Cooper pairs arise from traveling electron waves, which are mobile in all directions. However, the resistance of cuprates in the c …