Understanding Topological Insulators in Real Space.

Area of Science:

• Condensed Matter Physics
• Quantum Chemistry
• Materials Science

Background:

• The Su-Schrieffer-Heeger model is crucial for understanding polyacetylene's electronic properties.
• Topological insulator indices like IPR are limited in differentiating phases and analyzing real-space properties.
• Understanding electron delocalization is key to characterizing material phases and symmetries.

Purpose of the Study:

• To introduce a real-space understanding of the Su-Schrieffer-Heeger model using delocalization indices.
• To develop a method that goes beyond traditional topological insulator indices for phase differentiation.
• To provide a simple, orbital-invariant tool for analyzing chirality and topological behavior.

Main Methods:

• Utilized delocalization indices from the quantum theory of atoms in molecules.
• Focused on analyzing electron delocalization between second neighbors (δi,i+2).
• Investigated the impact of doping and structural changes (e.g., odd atom chains) on chirality.

Main Results:

• The second neighbor delocalization index (δi,i+2) effectively differentiates trivial and topological insulator phases.
• This index highlights the role of sublattices induced by chiral symmetry and identifies its presence or breaking.
• Hints for identifying bulk behavior using the δ1,3 index were provided.

Conclusions:

• A simple, orbital-invariant visualization tool based on delocalization indices aids in analyzing chirality.
• The approach facilitates the understanding of topological behavior, independent of system crystallinity.
• This method bridges concepts in chemistry and physics, promoting broader understanding of topological materials.