Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars

TL;DR

This paper uses Majorana's stellar representation to geometrically characterize topological phases in inversion-symmetric polymerized models, linking Majorana star trajectories to topological invariants.

Contribution

It introduces a geometrical interpretation of topological phases via Majorana star trajectories, providing a new perspective on topological characterization in polymerized models.

Findings

Majorana star trajectories differ between trivial and nontrivial phases.

Topological phases are determined by Majorana star distributions at high-symmetry points.

The geometrical structures of Majorana stars serve as indicators of topological properties.

Abstract

By using Majorana's stellar representation, we give a clear geometrical interpretation of the topological phases of inversion-symmetric polymerized models by mapping the Bloch states of multi-band systems to Majorana stars on the Bloch sphere. While trajectories of Majorana stars of a filled Bloch band exhibit quite different geometrical structures for topologically trivial and nontrivial phases, we further demonstrate that these structures are uniquely determined by distributions of Majorana stars of two high-symmetrical momentum states, which have different parities for topologically different states.