Disorder Induced Cluster Formation near First Order Phase Transitions in Electronic Systems: Importance of Long-Range Coulomb Interaction

We discuss the effects of fluctuations of the local density of charged dopants near a first order phase transition in electronic systems, that is driven by change of charge carrier density controlled by doping level. Using a generalization of the Imry-Ma argument, we find that the first order transition is rounded by disorder at or below the lower critical dimension d_c=3, when at least one of the two phases has no screening ability. The increase of d_c from 2 (as in the random field Ising model) to 3 is due to the long-range nature of the Coulomb interaction. This result suggests that large clusters of both phases will appear near such transitions due to disorder, in both two and three dimensions. Possible implications of our results on manganites and underdoped cuprates will be discussed.