Two-dimensional Discommensurations: an extension to McMillan's Ginzburg-Landau Theory

TL;DR

This paper extends McMillan's Ginzburg-Landau theory to two dimensions, providing exact solutions for discommensuration patterns and a framework for multi-component charge density waves in layered materials.

Contribution

It introduces a two-dimensional extension of discommensuration theory, enabling analysis of complex CDW patterns in quasi-two-dimensional systems.

Findings

Exact solutions for 2D discommensuration patterns

Framework for multi-component CDW in layered materials

Enhanced understanding of CDW phase transitions

Abstract

Charge density waves (CDW) profoundly affect the electronic properties of materials and have an intricate interplay with other collective states, like superconductivity and magnetism. The well-known macroscopic Ginzburg-Landau theory stands out as a theoretical method for describing CDW phenomenology without requiring a microscopic description. In particular, it has been instrumental in understanding the emergence of domain structures in several CDW compounds, as well as the influence of critical fluctuations and the evolution towards or across lock-in transitions. In this context, McMillan's foundational work introduced discommensurations as the objects mediating the transition from commensurate to incommensurate CDW, through an intermediate nearly commensurate phase characterised by an ordered array of phase slips. Here, we extend the simplified, effectively one-dimensional, setting of the original model to a fully two-dimensional analysis. We find exact and numerical solutions for several types of discommensuration patterns and provide a framework for consistently describing multi-component CDW embedded in quasi-two-dimensional atomic lattices.