Electronic structure of HgBa$_2$CuO$_{4+δ}$ with self-organized interstitial oxygen wires in the Hg spacer planes

Abstract: While recent experiments have found that at optimum doping for the highest critical temperature in HgBa$2$CuO${4+y}$ (Hg1201) the oxygen interstitials (O-i) are not homogeneously distributed but form one-dimensional atomic wires, there are no available information of its electronic structure considering self-organized O-i atomic wires. Here we report the calculated electronic structure of HgBa$2$CuO${4+y}$ where oxygen interstitials form atomic wires along (1,0,0) crystal direction in the Hg layer. We find that at optimum doping for superconductivity the chemical potential is tuned near an electronic topological Lifshitz transition for the appearing of a second quasi 1D Fermi surface. A $first$ large Fermi surface coexists with a $second$ incipient quasi one dimensional (1D) Fermi surface related with atomic wires of oxygen interstitials. Increasing oxygen doping the chemical potential is driven to the band edge of the $second$ 1D-band giving a peak in the density-of-states. The new 1D electronic states are confined near the oxygen interstitial wires with a small spread only on nearby sites. Spin-polarized calculations show that the magnetic response is confined in the oxygen-poor domains free of oxygen interstitials wires and it is quite insensitive to the density of O-i wires.