Switching Spinless and Spinful Topological Phases with Projective PT Symmetry

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Physical systems are fundamentally classified as spinless or spinful, impacting symmetry-protected topological phases.
• Spacetime inversion symmetry (PT) algebra differs between spinless ((PT)^2=1) and spinful ((PT)^2=-1) systems.
• Distinct topological phases are associated with each spin classification.

Purpose of the Study:

• To reveal a method for switching between spinless and spinful topological phase classifications.
• To enable the realization of topological phases in systems where they are typically forbidden.
• To explore novel topological phenomena by overcoming fundamental limitations.

Main Methods:

• Utilizing Z2 projective representations to alter the symmetry algebra.
• Investigating the condition where spacetime inversion (P) inverts gauge transformations for Z2 gauge connections.
• Developing concrete theoretical models to demonstrate the switching mechanism.

Main Results:

• Demonstrated the ability to achieve spinful topological phases in spinless systems and vice versa.
• Explicitly modeled Kramers degenerate bands and Kramers Majorana boundary modes in spinless systems.
• Showcased the realization of topological phases in spinful systems previously unique to spinless ones.

Conclusions:

• The developed Z2 projective representation method breaks fundamental limitations in topological phase research.
• This work opens unprecedented possibilities for realizing intriguing topological phases in diverse physical systems.
• Experimental realization of these novel topological phases is discussed, paving the way for future applications.