Multicellularity of Delicate Topological Insulators.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Chemistry

Background:

• Topological insulators are materials with unique electronic properties.
• Standard classification methods include the tenfold way and topological quantum chemistry.
• Wannier localization is a key concept in understanding topological phases.

Purpose of the Study:

• Introduce a new class of topological insulators.
• Challenge existing classification paradigms.
• Characterize a novel type of topological property termed 'delicate topology'.

Main Methods:

• Analysis of Wannier functions and their localization properties.
• Application of symmetry-based indicator methods.
• Investigation of band topology under perturbations.

Main Results:

• Identified topological insulators with symmetric, exponentially localized Wannier functions.
• Demonstrated that Wannier functions cannot be confined to a single unit cell.
• Classified this topology as 'delicate', distinct from stable or fragile types.

Conclusions:

• Wannierizability does not preclude non-trivial topology.
• Existing classification methods may overlook certain topological phases.
• Delicate topological phases are susceptible to disruption by trivial bands.