Three-dimensional [Formula: see text] topological insulators without reflection symmetry

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Symmetry Classification

Background:

• The Altland-Zirnabuer (AZ) table classifies topological insulators (TIs) by dimension and symmetry.
• Classifying 3D time-reversal symmetric TIs (class AII) without reflection symmetry remains a challenge.
• Existing methods often rely on specific crystalline symmetries or the AZ paradigm.

Purpose of the Study:

• To present a general procedure for constructing 3D topological insulators beyond the standard AZ classification.
• To explore topological phases with classifications not covered by the existing AZ table.
• To demonstrate the utility of projected topological branes (PTBs) for dimensional reduction and topological phase embedding.

Main Methods:

• Utilizing the framework of projected topological branes (PTBs).
• Constructing a 3D projected brane from a 4D topological insulator parent.
• Analyzing the topological classification via response to bulk monopole loops.

Main Results:

• A 3D projected brane from a 4D TI exhibits a [Formula: see text] topological classification.
• PTBs enable dimensional reduction and embedding of topological properties from higher dimensions.
• This approach yields lower-dimensional topological phases beyond the AZ classification without requiring additional symmetries.

Conclusions:

• Projected topological branes offer a novel route to realizing and classifying topological insulators.
• The findings extend the understanding of topological phases beyond established paradigms.
• This work has potential applications in metamaterials like photonic crystals and topolectric circuits.