Topologically constrained obstructed atomic limits in quasi-one-dimensional systems

TL;DR

This paper develops a group-theoretical framework to identify and classify obstructed atomic limits in quasi-one-dimensional systems, enhancing topological characterization methods with systematic analysis and illustrative examples.

Contribution

It introduces a theorem-based approach for analyzing obstructed atomic limits using line group symmetry in quasi-one-dimensional systems.

Findings

Systematic classification of obstructed atomic limits

A theorem linking symmetry and topological phases

Illustrative examples demonstrating the framework

Abstract

Possible forms of obstructed atomic limits in quasi-one-dimensional systems are studied using line group symmetry. This is accomplished by revisiting the standard theory with an emphasis on its group-theoretical background, synthesizing the insights into a theorem that effectively identifies potential cases. The framework is then applied across the classes of quasi-one-dimensional systems, where the obstructed atomic limit serves as the primary criterion for topological characterization. The results are systematically organized and displayed, complemented by several illustrative examples.