Non-Abelian Tensor Berry Connections in Multiband Topological Systems.

Area of Science:

• Condensed Matter Physics
• Theoretical Physics
• Materials Science

Background:

• Topological phases in multiband systems are crucial for novel quantum phenomena.
• Existing theories often struggle to unify diverse topological classifications.
• The emergence of gauge fields in condensed matter is a key area of research.

Purpose of the Study:

• Introduce and apply non-Abelian tensor Berry connections for topological phases.
• Generalize existing Berry connection formalisms to multiband systems.
• Provide a unifying framework for classifying topological matter.

Main Methods:

• Constructing non-Abelian antisymmetric tensor gauge fields from momentum-space Higgs fields.
• Deriving topological invariants using winding numbers associated with Higgs fields.
• Developing higher-dimensional Berry-Zak phases for topological characterization.

Main Results:

• Conventional topological invariants for 2D topological insulators and 3D Dirac semimetals are derived.
• Higher-dimensional Berry-Zak phases are constructed and applied to classify various gapped and gapless systems.
• A novel class of models supporting space-time inversion and chiral symmetries is identified.

Conclusions:

• Non-Abelian tensor Berry connections offer a unifying framework for multiband topological systems.
• This formalism sheds light on the emergence of non-Abelian gauge fields in condensed matter.
• The findings have direct implications for discovering new topological phases in solid-state and synthetic systems.