First-Principles Calculations of Electronic States and Self-Doping Effects at a 45° Grain Boundary in the High Temperature ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathbf{O}}_7$ Superconductor

The charge redistribution at grain boundaries determines the applicability of high-$T_c$ superconductors in electronic devices because the transport across the grains can be hindered considerably. We investigate the local charge transfer and the modification of the electronic states in the vicinity of the grain-grain interface by ab initio calculations for a (normal-state) 45°-tilted [001] grain boundary in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$. Our results explain the suppressed interface transport and the influence of grain boundary doping in a quantitative manner, in accordance with the experimental situation. The charge redistribution is found to be strongly inhomogeneous, which has a substantial effect on transport properties since it gives rise to a self-doping of $0.10\pm 0.02$ holes per Cu atom.

Figure 1

Structural setup used for simulating a 45° YBCO grain boundary (wiggly line), in a projection along the YBCO $c$ axis. Large spheres represent $\mathrm{Y}/\mathrm{Ba}$, medium spheres Cu, and small spheres O. Whereas the square highlights a YBCO unit cell, the outer rectangle indicates the boundaries of the supercell.

Figure 2

Left: partial Cu $3d$ and O $2p$ DOS for the entire supercell, normalized by the number of $\mathrm{Cu}/\mathrm{O}$ atoms. Center/right: site-projected DOS of selected sites in the 45° YBCO grain boundary: bulklike coordinated O (center; showing two examples) and Cu at the grain boundary compared to bulklike coordinated Cu (right; both on CuO chain sites).

Figure 3

Partial (site-projected) DOS of selected bulklike coordinated atoms in the 45° YBCO grain boundary, as compared to the corresponding YBCO bulk DOS: Cu in the ${\mathrm{CuO}}_2$ planes (left top), Cu in the CuO chains (left bottom), Y (right top), and Ba (right bottom).

Figure 4

Contour plots of the hole density, i.e., the integrated total DOS between the Fermi level and 1.9 eV, in the ${\mathrm{CuO}}_2$ planes of bulk YBCO (left) and of the supercell (right). The display area is the square shown in Fig. 1, with Cu in the corners and O in the centers of the edges.