Competing orders suppressed by disorder around a hidden quantum critical point in high-T c cuprate superconductors

We report extensive muon-spin-rotation measurements on the lightly doped Y1-xCaxBa2Cu3O6+y compound, which allows us to disentangle the effect of disorder, controlled by random Ca2+ substitution, from that of mere doping. A three-dimensional phase diagram of lightly doped cuprates is accurately drawn. It shows a quantum critical point around which a thermally activated antiferromagnetic phase competes with superconductivity. Disorder suppresses both the competing order parameters and the quantum critical point, unveiling an underlying frozen state.