Ill-defined Topological Phases in Dispersive Photonic Crystals

TL;DR

This paper investigates the limitations of topological classification in dispersive photonic crystals, revealing conditions under which traditional topological invariants become ill-defined and proposing regularization methods to address these issues.

Contribution

It uncovers the breakdown of topological methods in dispersive photonic systems and introduces two regularization techniques to properly define their topology.

Findings

Chern numbers can be non-integer in plasmonic systems.

Nonlocal effects are crucial for well-defined topology.

Regularization methods depend on bulk material response at large wavevectors.

Abstract

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with little modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break-down and the Chern topology becomes ill-defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be non-integer notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk-materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large k.