Lattice on Lattice in Two Dimensions

TL;DR

This paper investigates how a harmonic triangular lattice responds to a weak periodic potential, revealing short-range positional order but persistent long-range orientational order, with implications for understanding hexatic phases in various materials.

Contribution

It demonstrates that elastic lattices can exhibit short-range positional correlations while maintaining long-range orientational order under weak periodic perturbations.

Findings

Positional correlations are short-ranged despite no defects.

Long-range orientational order persists.

Provides explanation for hexatic glass phases in materials.

Abstract

We study a harmonic triangular lattice, which relaxes in the presence of a weak, short-wavelength periodic potential. Monte Carlo simulations reveal that the elastic lattice has only short-ranged positional correlations, despite the absence of defects in either lattice. Long-range orientational order, however, persists in the presence of the background. Our results provide an alternative explanation for the hexatic glassphase observed in high-temperature superconductors, magnetic bubble lattices, and charge density waves in semiconductors.