Enhanced stability of the square lattice of a classical bilayer Wigner crystal

TL;DR

This study investigates the stability and melting behavior of bilayer Wigner crystals with various lattice structures, revealing that the square lattice exhibits notably higher melting temperatures due to defect topology.

Contribution

It introduces a universal melting criterion applicable to different inter-particle interactions and provides a comprehensive phase diagram for bilayer Wigner crystals.

Findings

Square lattice has higher melting temperature than other structures.

Universal melting criterion applicable to various interactions.

Phase diagram shows dependence on interlayer distance.

Abstract

The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the Monte-Carlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and 1/r^{12} repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the interlayer distance. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures. This is a consequence of the specific topology of the defects which are created with increasing temperature and which have a larger energy as compared to the defects in e.g. a hexagonal lattice.