Structural phase transitions in low-dimensional ion crystals

TL;DR

This paper analyzes the second-order phase transition in low-dimensional ion crystals from a linear chain to a zigzag configuration, using Landau theory to match numerical predictions and determine behavior at the critical point.

Contribution

It provides an analytical Landau theory description of the structural phase transition in ion crystals, confirming numerical results and characterizing the transition's behavior.

Findings

Analytical expression for the transition point.

Agreement with previous numerical predictions.

Characterization of the order parameter at the transition.

Abstract

A chain of singly-charged particles, confined by a harmonic potential, exhibits a sudden transition to a zigzag configuration when the radial potential reaches a critical value, depending on the particle number. This structural change is a phase transition of second order, whose order parameter is the crystal displacement from the chain axis. We study analytically the transition using Landau theory and find full agreement with numerical predictions by [J. Schiffer Phys. Rev. Lett. 70, 818 (1993)] and [Piacente et al Phys. Rev. B 69, 045324 (2004)]. Our theory allows us to determine analytically the system's behaviour at the transition point.