Areas of superconductivity and giant proximity effects in underdoped cuprates

Phenomenological models for the antiferromagnetic (AF) versus d-wave superconductivity competition in cuprates are studied using conventional Monte Carlo techniques. The analysis suggests that cuprates may show a variety of different behaviors in the very underdoped regime: local coexistence or first-order transitions among the competing orders, stripes, or glassy states with nanoscale superconducting (SC) puddles. The transition from AF to SC does not seem universal. In particular, the glassy state leads to the possibility of "colossal" effects in some cuprates, analog of those in manganites. Under suitable conditions, nonsuperconducting Cu-oxides could rapidly become superconducting by the influence of weak perturbations that align the randomly oriented phases of the SC puddles in the mixed state. Consequences of these ideas for thin-film and Photoemission experiments are discussed.