Compatibility of distortion fields caused by topological defects in 2D latties

TL;DR

This paper investigates the geometric compatibility of distortion fields caused by topological defects in 2D lattices, establishing conditions under which such defects can exist without violating lattice integrity.

Contribution

It formulates criteria for the geometric compatibility of lattice distortions and demonstrates the existence of compatible, homotopically non-trivial distortion fields in 2D lattices.

Findings

Criteria for geometric compatibility of lattice distortions are established.

Compatible, homotopically non-trivial distortion fields exist in 2D lattices.

Theoretical framework for topological defects in 2D crystalline lattices.

Abstract

Topological defects in crystalline lattices are considered. In relation to physical realizability of such defects, criteria for geometric compatibility of the lattice distortions are formulated. For 2D lattices it is shown that the answer to the question of existence of distortion fields which are both geometrically compatible and homotopically non-trivial is in the affirmative.