Inhomogeneous states in two-dimensional frustrated phase separation

TL;DR

This paper analyzes the phase diagram of Coulomb frustrated phase separation in two-dimensional systems, revealing the nature of phase transitions and the formation of inhomogeneous structures.

Contribution

It provides a detailed theoretical derivation of the phase diagram considering different Coulomb interactions and describes the topology of inhomogeneous states.

Findings

Transition from homogeneous to inhomogeneous phase is mostly first-order.

Inhomogeneities form a triangular lattice near the critical point.

A topological transition to stripe-like objects occurs with reduced Coulomb frustration.

Abstract

We derive the phase diagram of a paradigmatic model of Coulomb frustrated phase separation in two-dimensional systems with negative short-range electronic compressibility. We consider the system subject either to the truly three-dimensional long-range Coulomb interaction (LRC) and to a two-dimensional LRC with logarithmic-like behavior. In both cases we find that the transition from the homogeneous phase to the inhomogeneous phase is generically first-order except for a critical point. Close to the critical point, inhomogeneities arrange in a triangular lattice with a subsequent first-order topological transition to stripe-like objects by lowering the Coulomb frustration. A proliferation of inhomogeneities which have inside smaller inhomogeneities is expected near all the transition lines in systems embedded in the three-dimensional LRC alone.