Detailed analysis of the Bi-O pockets problem in $Bi_2Sr_2Ca_2Cu_3O_{10}$

Abstract

The Bi-O pockets problem, namely, the appearance in theoretical ab initio calculations of the electronic band structure of Bi-cuprates of a pocket of states at the Fermi energy ($E_F$) that is attributed to states belonging to the Bi-O plane is an issue that still calls for more study. The Bi-O pockets are in contradiction with experiments. We have investigated the possible reasons for the disagreement. We checked that by using the experimental lattice and internal parameters without any optimization procedure, the Bi-O pockets do not appear at $E_F$ in agreement with experiment. Nevertheless, as pointed out by R. Kouba et al. [{\em Phys. Rev. B} {\bf 60}, 9321 (1999)] optimization is compulsory to a band structure calculation that will describe appropriately the electronic properties. But starting with the experimental parameters a further optimization procedure previous to the actual ab initio calculation leads to the Bi-O pockets. Doping with 25% of Pb they disappear. From the several configurations that we have considered, we found two very simple ways in which the Bi-O pockets disappear without avoiding an optimization procedure previous to the calculation and without including a doping of any kind. In this paper, we report the effect of the slight displacement of the oxygen atom associated to the Sr-plane (O3) in the electronic properties of $Bi_2Sr_2Ca_2Cu_3O_{10}$ (Bi-2223) with tetragonal structure ($I4/mmm$) using the Local Density Approximation (LDA). The slight displacement is performed after the system has been optimized. We determined the intervals of the O3 atomic positions for which calculations of the band structures show that the Bi-O bands emerge towards higher energies in agreement with the experimental results, thereby solving the Bi-O pockets problem (continue).