Self-generated electronic heterogeneity and quantum glassiness in the high-temperature superconductors

We present a systematic study of the spin and charge dynamics of copper oxide superconductors as a function of carrier concentration x. Our results portray a coherent physical picture, which reveals a quantum critical point at optimum doping (x=x(opt)), and the formation of a glassy state at x < x(opt). This mechanism is argued to arise as an intrinsic property of doped Mott insulators, and therefore to be largely independent of material quality and level of disorder.