Interplay of Ca and O doping in Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{6+y}$ studied by first-principles calculations

Experiments reveal an impressive asymmetry in most aspects (involving e.g. magnetic, superconducting, or structural properties) of high-Tc superconductors upon cation or oxygen doping, respectively. A thorough understanding of this asymmetry cannot eschew a rigorous description of the fundamental mechanism ruling electronic and structural properties for each (x,y) doping combination. Here we present results obtained by the pseudo-self-interaction free density functional (pSIC) method, which is capable to describe metal-insulating transitions in several cuprate materials. We describe in detail the chemistry of the distinct insulating-metal transitions occurring in the CuO chains and in the CuO$_{2}$ planes in underdoped YBa$_{2}$Cu$_{3}$O$_{6+y }$for y=[0,0.5]. We then show that interactions with chains crucially affect the ability of Ca doping to inject holes in CuO$_{2}$ planes. The dramatic effects of this double-doping interplay on the magnetic and superconducting properties of underdoped Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{6+y}$ cannot be understood by the disentangled action of the individual doping sources.