Ginzburg-Landau theory of the zig-zag transition in quasi-one-dimensional classical Wigner crystals

Abstract

We present a mean-field description of the zig-zag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential $r^{-n}{e}^{-r/\lambda }$, that are confined by a power-law potential ($y^{\alpha }$). The parameters of the resulting one-dimensional Ginzburg-Landau theory are determined analytically for different values of $\alpha$ and $n$. Close to the transition point for the zig-zag phase transition, the scaling behavior of the order parameter is determined. For $\alpha =2$ the zig-zag transition from a single to a double chain is of second order, while for $\alpha >2$ the one chain configuration is always unstable and for $\alpha <2$ the one chain ordered state becomes unstable at a certain critical density resulting in jumps of single particles out of the chain.

12 pages, 11 figures

References in corpus (6)

• Structural phase transitions in low-dimensional ion crystals
• Wigner crystal physics in quantum wires
• Spontaneous nucleation of structural defects in inhomogeneous ion chains
• Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires
• Wigner crystals of ions as quantum hard drives
• Quantum phase transition in quantum wires controlled by an external gate

Cited by in corpus (2)

• Generic ordering of structural transitions in quasi-one-dimensional Wigner crystals
• Structural transitions in vertically and horizontally coupled parabolic channels of Wigner crystals