Model of Coulomb-limited phase separation

The phenomenon of Coulomb limited phase separation is found in many lightly doped insulators. It has come to focus with the discovery of high-temperature superconductors, as first noted in the seminal work of Gor'kov and Sokol.

This JAVA applet (REQUIRES THE LATEST VERSION OF JAVA 1.7) presents a simulation of a classical liquid with competing interactions: long-range Coulomb repulsion V(R)=1/R and a finite-range uniform attaction of strength V and range R_o. The simulation is implemented on a partially-filled square lattice, using Monte Carlo methods. By default, when the simulation starts, the system shows a lattice at 40% filling, but the filling can be modified, if desired by either entering the number of electron or the filling (between 0 and 1) into the "# of Electrons/Filling" box

We can change the initial coniditions to either random, striped or crystalline.

We can add frozen impurities with tunable charge Q, which can be chosen to be positive or negative. This can be used to investigate how the frozen impurities affect the freezing/melting.

We can create a random disorder in the system, by adding M frozen impurities. These impurities have randomly distributed charges between -W/2 and W/2, where W is the "Strength Parameter."

We can add an external electric field of strength E, which can be chosen to be positive or negative.

We can also turn off  and on  the repulsive Coulomb interactions, and control the strength V and the range R_o of the attraction.

Stripes, Bubbles, or Stripe Glass?

This simulation can be used to visualize the phenomenon of Coulomb-limited phase separation. In absence of the Coulomb repulsion, the attraction would, at low temperature, lead to phase separation, where the particles "condense" into high-density liquid droplets. As time progresses, these droplets merge into bigger and bigger clusters, displaying "spinodal decomposition".  This process can be visualized by turning off the Coulomb repulsion (pressing the Coulomb repulsion: off button). If the Coulomb interactions are turned on, they will prevent the emergence of droplets larger then a characteristic size controlled by the charging effect. As the system is colled, different patter then emerge: bubbles or stripes, depending on the density (filling). The lowest energy configuration, for a given density, corresponds to a periodic arrangement such bubbles or stripes - a bubble or stripe crystal. However, crystalization takes place through a first order phase transition, and is difficult to achieve (requires very long nucleation times). If the system is cooled sufficiently quickly, the periodic ordering is not achieved; the system then freezes into an amorphous solid - "the stripe glass". The tendency to avoid periodic patterns is further suppressed if we add a small concentration of impurities at random positions.

This JAVA applet can be used to visualize the formation and dynamics of these complex states of matter, and examine how they are affected by random impurities and external electric fields.

Created by Eric Pelz with the help of Graduate Student Yohanes Pramudya and Professors Vladimir Dobrosavljevic, Stratos Manousakis and Jorge Piekarewicz at the National Magnetic Field Laboratory at the Florida State University. Updated by Marshall Jiang.