Phase Competition and Inhomogeneous States as a New Paradigm for Complex Materials

A new paradigm in the study of complex materials is gaining considerable experimental and theoretical support. It is based on the notion that many unusual properties of these materials arise from the competition of phases, often involving a metal and an insulator. A family of materials these effects are very clear are the manganites, that exhibit the colossal magnetoresistance effect. Recent theoretical work has shown that this effect is caused by phase competition between a double-exchange metal and a charge-ordered insulator. But this competition is certainly not restricted to manganites but arises in many other contexts such as underdoped high-Tc cuprates, where the pseudogap phase could also be a mixture of superconducting and antiferromagnetic regions. In this chapter, a generic description of these effects is presented and the typical consequences of phase competition are outlined.