The influence of proximity effects in inhomogeneous electronic states

We describe the high-temperature superconductor La$_{2-x}$Sr$_x$CuO$_4$ in the underdoped regime in terms of a mixed-phase model, which consists of superconducting clusters embedded in the antiferromagnetic matrix. Our work is motivated by a series of recent angle-resolved photoemission experiments, which have significantly enhanced our understanding of the electronic structure in single-layer cuprates, and we show that those results can be fully reproduced once a reasonable set of parameters is chosen and disorder is properly taken into account. Close to half-filling, many nominally hole-rich and superconducting sites have comparatively large excitation gaps due to the ubiquitous proximity of the insulating phase. No other competing states or any further assumptions are necessary to account for a satisfying description of the underdoped phase, including the notorious pseudogap, which emerges as a natural consequence of a mixed-phase state. Close to optimal doping, the resulting gap distribution mirrors the one found in tunneling experiments. The scenario presented is also compelling because the existence of an optimal doping is intrinsically linked to the presence of electronic inhomogeneity, as is the transition from the highly mysterious to the rather conventional nature of the metallic state above $T_c$ in the overdoped regime. The phase diagram that emerges bears strong similarity to the canonical cuprate phase diagram, it explains quantitatively the rapid loss of long-range antiferromagnetic order, and also provides for a ``superconducting fluctuating'' regime just above $T_c$ as recently proposed in the context of resistance measurements. Implications for manganites are briefly discussed.