Ryzhov’s Defect Formalism on A Rigid-Slip Strip: Dislocations in an Ideal Quasi-One-Dimensional Wigner Crystal

Abstract

We extend Ryzhov’s defect formalism for two-dimensional melting to a triangular crystal confined between two parallel rigid-slip walls. The elastic Green function of the strip is obtained in closed form. Its mode that is uniform across the channel separates elementary dislocations into two physically distinct sectors. Longitudinal glide defects interact only over a distance set by the channel width and therefore produce a finite-size positional crossover. Oblique defects terminate a lattice row and act as domain walls between states with adjacent row numbers; their thermal population rounds the structural conversion on an activated scale. Positional disorder and row-number conversion are consequently different crossovers and need not occur together. The results provide a controlled reference problem for interpreting structural trends in confined electron crystals while also showing why realistic electrostatic channels require a different Green function.