Wallpaper fermions and the nonsymmorphic Dirac insulator

Area of Science:

• Condensed Matter Physics
• Materials Science
• Crystallography

Background:

• Topological crystalline insulators possess surface states protected by crystal symmetries.
• Existing topological crystalline insulators are categorized by limited surface crystal symmetries, described by 17 wallpaper groups.
• Understanding symmetry-allowed band degeneracies is crucial for classifying these materials.

Purpose of the Study:

• To utilize wallpaper groups and symmetry-allowed band degeneracies for classifying topological crystalline insulators.
• To predict novel topological crystalline insulator phases beyond previously described examples.
• To identify specific materials exhibiting these predicted topological phases.

Main Methods:

• Analysis of symmetry-allowed band degeneracies within the 17 wallpaper groups.
• Theoretical investigation of topological insulating phases arising from specific symmetry constraints.
• Prediction of material candidates based on theoretical findings, focusing on Sr2Pb3.

Main Results:

• A new topological insulating phase is identified, characterized by a single, fourfold-degenerate, true Dirac fermion.
• This phase arises in wallpaper groups with multiple glide lines (pgg and p4g).
• The predicted phase represents an exception to the symmetry-enhanced fermion-doubling theorem.

Conclusions:

• Consideration of wallpaper groups and band degeneracies provides a framework for understanding and predicting topological crystalline insulators.
• The identified topological phase with a single Dirac fermion offers a distinct platform for exploring topological phenomena.
• Sr2Pb3 in space group 127 (P4/mbm) is theoretically predicted to host this novel topological insulating phase.