Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Topological Phases of Matter

Background:

• Traditional topological materials characterization relies on symmetry, but novel multi-gap dependent topological states present challenges.
• These multi-gap states possess properties beyond existing symmetry-based approaches and require further exploration.
• While studied at equilibrium, their behavior in out-of-equilibrium conditions remains largely uncharted.

Purpose of the Study:

• To investigate the interplay between out-of-equilibrium processes and multi-gap topological insights.
• To explore novel topological phases induced by periodic driving that lack static counterparts.
• To identify and characterize new topological invariants and phases in dynamical systems.

Main Methods:

• Applying periodic driving (Floquet engineering) to multi-gap topological systems.
• Identifying and analyzing Floquet-induced non-Abelian braiding phenomena.
• Characterizing topological phases using invariants like the Euler class and investigating anomalous Dirac string configurations.

Main Results:

• Periodic driving induces anomalous multi-gap topological properties absent in static systems.
• Floquet-induced non-Abelian braiding is identified, leading to a phase with an anomalous Euler class.
• The first example of an 'anomalous Dirac string phase' is discovered, characterized by unique edge states.

Conclusions:

• Periodic driving is a powerful tool for discovering and controlling novel multi-gap topological phases.
• The findings provide a foundation for exploring intrinsically dynamical and experimentally accessible topological matter.
• Periodic driving facilitates the observation of non-Abelian braiding processes, particularly in quantum simulators.