Self-organization of charged particles on a two-dimensional lattice subject to anisotropic Jahn-Teller-type interaction and three-dimensional Coulomb repulsion

Abstract

Self-organization of charged particles on a two-dimensional lattice, subject to an anisotropic Jahn-Teller-type interaction and three-dimensional Coulomb repulsion, is investigated. In the mean-field approximation without Coulomb interaction, the system displays a phase transition of first order. In the presence of the Coulomb repulsion, the global phase separation becomes unfavorable and the system shows a mesoscopic phase separation, where the size of the charged regions is determined by the competition between the ordering energy and the Coulomb energy. The phase diagram of the system as a function of particle density and temperature is obtained by systematic Monte Carlo simulations. With decreasing temperature, a crossover from a disordered state to a state composed of mesoscopic charged clusters is observed. In the phase separated state, charged clusters with even number of particles are more stable than those with odd number of particles in a large range of particle densities. With increasing particle density at low temperatures, a series of crossovers between states with different cluster sizes is observed. Above half-filling, in addition to the low temperature clustering, another higher temperature scale, which corresponds to orbital ordering of particles, appears. We suggest that the diverse functional behavior observed in transition metal oxides can be thought to arise from the self-organization of this type.