Inhomogeneity effects in oxygen-doped $\mathrm{Hg}{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_4$

We theoretically investigate inhomogeneity effects on the charges, electric field gradients, and site-projected densities of states in $\mathrm{Hg}{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_{4+\delta }$. We find pronounced differences in the doping-induced number of holes at different atomic sites. The contributions of these sites to the density of states in the vicinity of the Fermi level are peaked at the same energy, but vary in magnitude by up to 70% and have a different energy dependence. Due to this energy dependence the role of the intrinsic inhomogeneities for superconductivity strongly depends on the energy and character of the quasiparticle mediating the Cooper pairing. Our results can explain the origin of doping-induced effects observed either by local or macroscopic experimental probes.

Figure 1

(Color online) Copper-oxygen planes of the $\mathrm{Hg}{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_{4+\delta }$ supercells representing the doping concentrations of $\delta =0.125$ (upper left panel), 0.167 (upper right panel), 0.22 (lower left panel), and 0.25 (lower right panel). The unit cells are indicated by the bold gray lines, the copper (oxygen) atoms by the red (blue) spheres. The projection of the dopant oxygen (located at the Hg plane) onto these planes is marked by the gray circles. In the lowest panel, an alternative structure for $\delta =0.25$ is displayed.

Figure 2

(Color online) Selected $\mathrm{Cu}\left(d_{x^2-y^2}\right)$ and $\mathrm{O}\left(p_x\right)$ contributions to the density of states in states per eV stemming from the respective atomic spheres for two different doping concentrations. The vertical lines indicate the Fermi level.