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

Abstract Possible forms of obstructed atomic limits (OALs) in quasi-one-dimensional (quasi-1D) systems are studied within the framework of 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 efficiently identifies potential cases. The framework is then applied across the classes of quasi-1D systems, where the OAL serves as the primary criterion for topological characterization. The results are systematically organized and displayed, supported by a series of illustrative examples for clarity and insight.