Structural transitions in vertically and horizontally coupled parabolic channels of Wigner crystals

TL;DR

This paper investigates structural phase transitions in coupled Wigner crystal channels using Monte Carlo simulations, revealing complex phase diagrams and mode behaviors influenced by channel coupling and particle density.

Contribution

It provides the first detailed analysis of phase transitions in vertically and horizontally coupled parabolic channels of Wigner crystals, including a Ginzburg-Landau theory for the zigzag transition.

Findings

Rich phase diagram with continuous and discontinuous transitions in vertical coupling.

Limited phase transitions due to symmetry in horizontal coupling.

Zigzag transition occurs only at low densities in vertical systems.

Abstract

Structural phase transitions in two vertically or horizontally coupled channels of strongly interacting particles are investigated. The particles are free to move in the $x$-direction but are confined by a parabolic potential in the $y$-direction. They interact with each other through a screened power-law potential ($r^{-n}e^{-r/\lambda}$). In vertically coupled systems the channels are stacked above each other in the direction perpendicular to the $(x,y)$-plane, while in horizontally coupled systems both channels are aligned in the confinement direction. Using Monte Carlo (MC) simulations we obtain the ground state configurations and the structural transitions as a function of the linear particle density and the separation between the channels. At zero temperature the vertically coupled system exhibits a rich phase diagram with continuous and discontinuous transitions. On the other hand the vertically coupled system exhibits only a very limited number of phase transitions due to its symmetry. Further we calculated the normal modes for the Wigner crystals in both cases. From MC simulations we found that in the case of vertically coupled systems the zigzag transition is only possible for low densities. A Ginzburg-Landau theory for the zigzag transition is presented, which predicts correctly the behavior of this transition from which we interpret the structural phase transition of the Wigner crystal through the reduction of the Brillouin zone.