Electronic properties and chain conductivity of underdoped YBa$_2$Cu$_3$O$_{6+x}$ by First-Principles calculations

Metal-insulating transitions in cuprates represent an historical challenge for first-principles calculations. Here we present results obtained through the pseudo-self-interaction free density functional scheme (PSIC) that is capable to correct the gross failures of LSDA at just a moderate increase of computing effort, and works well in both strong-correlated and metallic limit. Here we describe the properties of the end-point systems YBa$_2$Cu$_3$O$_6$ and YBa$_2$Cu$_3$O$_7$ as well as the chemistry of insulating-metal transition occurring in the CuO chains of underdoped YBa$_2$Cu$_3$O$_{6+x}$ in the region x=[0,0.5]. Coherently with the one-dimensional metallic percolative regime observed at low-doping, we find that the metal-insulating transition occurring at low doping in the non-magnetic Cu(1)Ox chains is induced by chain-like alignment of the doping oxygens within the chains, whereas disorder (i.e. non chain-aligned) distributions are always insulating. In the Cu(2)O2 planes the insulating antiferromagnetic state remains stable up to x=0.25, while at x=0.5 a normal-metal state, similar to that seen for YBa$_2$Cu$_3$O$_7$, take place. The in-plane antiferromagnetic- paramagnetic competition depends on x but is almost unaffected by the intra-chain order-disorder competition.