Ab initio evidence for the formation of impurity d_3z2-r2 holes in doped La_2-xSr_xCuO₄

Using the spin unrestricted Becke-3-Lee-Yang-Parr density functional, we computed the electronic structure of explicitly doped La_2-xSr_xCuO₄ (x = 0.125, 0.25, and 0.5). At each doping level, an impurity hole band is formed within the undoped insulating gap. This band is well localized to CuO₆ octahedra adjacent to the Sr impurities. The nature of the impurity hole is A_1g in symmetry, formed primarily from the z² orbital on the Cu and p_z orbitals on the apical O's. There is a strong triplet coupling of this hole with the intrinsic B_1g Cu x²-y²/O1 P_σ hole on the same site. Optimization of the c coordinate of the apical O's in the doped CuO₆ octahedron leads to an asymmetric anti-Jahn-Teller distortion of the O2 atoms toward the central Cu. In particular, the O2 atom between the Cu and Sr is displaced 0.26 Å while the O2 atom between the Cu and La is displaced 0.10 Å. Contrary to expectations, investigation of a 0.1 Å enhanced Jahn-Teller distortion of this octahedron does not force formation of an x²-y² hole, but instead leads to migration of the z² hole to the four other CuO₆ octahedra surrounding the Sr impurity. This latter observation offers a simple explanation for the bifurcation of the Sr-O2 distance revealed in x-ray absorption fine structure data.