Ground state structure of a bilayer Wigner crystal with repulsive dielectric images

TL;DR

This paper investigates how dielectric discontinuities affect the ground-state structures of bilayer Wigner crystals, revealing new phase behaviors and energy minima due to repulsive image charges.

Contribution

It provides the first complete phase diagram for bilayer Wigner crystals considering dielectric jumps and repulsive images, extending previous homogeneous dielectric models.

Findings

Particles form a monolayer up to a critical distance.

A bifurcation leads to bilayer structures beyond this distance.

The ground-state energy shows a global minimum at a specific separation.

Abstract

We study the ground-state structures of identical classical point charges with Coulomb interactions, confined between two symmetric parallel charged walls. For the well understood homogeneous dielectric case with no electrostatic images, the charges evenly condense on the opposite walls, thereby forming a bilayer Wigner crystal; five structures compete upon changing the inter-wall separation. Here, we consider a dielectric jump between the walls and a solvent in which charges are immersed, implying repulsive images. Using recently developed series representations of lattice sums for Coulomb law, we derive the complete phase diagram. In contrast to the homogeneous dielectric case, the particles remain in a hexagonal Wigner monolayer up to a certain distance between the walls. Beyond this distance, a bifurcation occurs to a sequence of Wigner bilayers, each layer having a nonzero spacing from the nearest wall. Another new phenomenon is that the ground-state energy as a function of the wall separation exhibits a global minimum.