Stability, dynamical properties and melting of a classical bi-layer Wigner Crystal

TL;DR

This paper studies the stability, dynamics, and melting behavior of a classical bi-layer Wigner crystal, revealing a complex phase diagram with multiple stable phases and analyzing phonon excitations and melting temperatures.

Contribution

It provides a detailed analysis of phase stability, transitions, and melting in a bi-layer Wigner crystal, including phonon calculations and free-energy minimization.

Findings

Five stable crystalline phases identified

Phase boundaries include continuous and discontinuous transitions

No temperature-induced structural phase transition found

Abstract

We investigate the stability, the dynamical properties and melting of a two-dimensional (2D) Wigner crystal (WC) of classical Coulombic particles in a bi-layer structure. Compared to the single-layer WC, this system shows a rich phase diagram. Five different crystalline phases are stable; the energetically favoured structure can be tuned by changing either the inter-layer distance or the particle density. Phase boundaries consist of both continuous and discontinuous transitions. We calculated the phonon excitations of the system within the harmonic approximation and we evaluated the melting temperature of the bi-layer WC by use of a modified Lindemann criterion, appropriate to 2D systems. We minimized the harmonic free-energy of the system with respect to the lattice geometry at different values of temperature/inter-layer distance and we found no temperature-induced structural phase transition.