Ill-Defined Topological Phases in Local Dispersive Photonic Crystals.

Area of Science:

• Condensed matter physics
• Photonics
• Topological materials

Background:

• Topological band theory, initially for condensed matter, applies to optical systems.
• Mathematical equivalence is usually assumed between condensed matter and optical topological classifications.

Purpose of the Study:

• Investigate breakdowns in standard topological methods for optical systems.
• Address challenges posed by particle-hole symmetry and dispersive nonreciprocal photonic materials.
• Develop regularization techniques for well-defined topological characterization.

Main Methods:

• Analysis of particle-hole symmetry and dispersive effects in nonreciprocal photonic materials.
• Examination of Chern topology and gap Chern numbers in plasmonic systems.
• Proposal and evaluation of two regularization methods for topological characterization.

Main Results:

• Standard topological methods can break down for optical systems with particle-hole symmetry and dispersion.
• Gap Chern numbers may become noninteger in plasmonic systems due to diverging photonic state densities.
• Nonlocal effects in bulk materials are crucial for well-defined topology in dispersive photonic crystals.

Conclusions:

• Topological classification in optics requires careful consideration of material properties and symmetries.
• Regularization methods are essential for defining topology in challenging optical systems.
• The proposed methods highlight the critical dependence of regularized topologies on bulk material response.