Ewald sum for electronic bilayer systems

Strong-Coupling Phases of Trions and Excitons in Electron-Hole Bilayers at Commensurate Densities

We introduce density imbalanced electron-hole bilayers at a commensurate 2:1 density ratio as a platform for realizing novel phases of electrons, excitons, and trions. Through the independently tunable carrier densities and interlayer spacing, competition between kinetic energy, intralayer repulsion, and interlayer attraction yields a rich phase diagram. By a combination of theoretical analysis and numerical calculation, we find a variety of strong-coupling phases in different parameter regions, including quantum crystals of electrons, excitons, and trions. We also propose an "electron-exciton supersolid" phase that features electron crystallization and exciton superfluidity simultaneously. The material realization and experimental signature of these phases are discussed in the context of semiconductor transition metal dichalcogenide bilayers.

Generalized approach to Ewald sums

We derive Ewald sum formulas for potential energy and force for a system of point charges interacting with an arbitrary, long-range central potential. The system is made neutral by a uniform background of opposite charge interacting with the same potential. These formulas can be readily used in computer numerical simulations of model physical systems. In particular, expressions for the potential energy and the force have been obtained in both two and three dimensions for Coulomb and other power-law potentials, Yukawa systems, and for an electronic bilayer. We discuss numerical results and their accuracy for various systems and, based on our analysis, suggest values to be used for the parameters that appear in the Ewald sums.

Molecular dynamics study of a bilayer electron gas: single particle properties

The single-particle dynamical properties of a strongly coupled, classical, symmetric electronic bilayer system have been investigated by molecular dynamics simulation. Results for the velocity correlation function, the single-particle scattering function, and their respective Fourier transforms have been calculated, and their behavior, as a function of the interlayer separation d, has been analyzed. The single-particle scattering function in particular, shows dramatic effects when the bilayer attains a staggered square lattice structure. This occurs when the interlayer separation is around 0.8a (a is the Wigner-Seitz radius), where our previous study showed a marked decrease in the diffusion coefficient.

Molecular dynamics study of diffusion in a bilayer electron gas

Molecular dynamics simulations of strongly coupled, classical electronic bilayers, interacting through the Coulomb potential, have been produced and studied. Values of the plasma coupling parameter Gamma between 10 and 80 and interlayer separations d from 0.1 to 3.0, (in units of Wigner-Seitz radius), were considered. The simulation results were used to calculate the intralayer and interlayer pair correlation functions and self-diffusion of charged particles in this system. The variation of self-diffusion with Gamma and d has been analyzed, and it is found that for the largest value of Gamma, the diffusion coefficient does not increase monotonically with layer separation, but has a distinct minimum for values of d slightly less than 1.