Ground state of classical bilayer Wigner crystals

TL;DR

This paper investigates the ground state configurations of classical bilayer Wigner crystals, deriving new energy representations and clarifying phase transitions to resolve previous inconsistencies in the literature.

Contribution

It introduces new series representations for Coulomb energies and provides a comprehensive analysis of phase transitions in bilayer Wigner crystals.

Findings

Derived highly convergent series for Coulomb energies.

Mapped the complete phase transition scenario including critical phenomena.

Unified previous conflicting results in the literature.

Abstract

We study the ground state structure of electronic-like bilayers, where different phases compete upon changing the inter-layer separation or particle density. New series representations with exceptional convergence properties are derived for the exact Coulombic energies under scrutiny. The complete phase transition scenario --including critical phenomena-- can subsequently be worked out in detail, thereby unifying a rather scattered or contradictory body of literature, hitherto plagued by the inaccuracies inherent to long range interaction potentials.