Abstract
Many topologically non-trivial systems have been recently realized using electromagnetic, acoustic, and other classical wave-based platforms. As the simplest class of three-dimensional topological systems, Weyl semimetals have attracted significant attention in this context. However, the robustness of the topological Weyl state in the presence of dissipation, which is common to most classical realizations, has not been studied in detail. In this paper, we demonstrate that the symmetry properties of the Weyl material play a crucial role in the annihilation of topological charges in the presence of losses. We consider the specific example of a continuous plasma medium and compare two possible realizations of a Weyl-point dispersion based on breaking time-reversal symmetry (reciprocity) or breaking inversion symmetry. We theoretically show that the topological state is fundamentally more robust against losses in the nonreciprocal realization. Our findings elucidate the impact of dissipation on three-dimensional topological materials and metamaterials.
Highlights
Weyl semimetals are a new class of materials with linear degeneracies in the three-dimensional momentum space, called Weyl points, which carry a topological charge and are sources or sinks of Berry curvature
For a non-Hermitian perturbation that is isotropic and independent of the wave vector, a Weyl point carrying unit topological charge is transformed into a planar ring of exceptional points [23]
For the time-reversal-broken case, we show in the following that the rings are located on distinct parallel planes and the presence of losses does not typically result in a topological transition
Summary
Weyl semimetals are a new class of materials with linear degeneracies in the three-dimensional momentum space, called Weyl points, which carry a topological charge and are sources or sinks of Berry curvature. It is well established that the Weyl semimetal state is extremely robust to perturbations This stems from the fact that Hermitian perturbations to the system’s Hamiltonian can only move Weyl points around in momentum space, without changing the topology of the system. One can imagine different scenarios in which nearby Weyl exceptional rings may come into contact in the presence of losses if the rings lie on the same plane in momentum space, or avoid each other completely if they lie on distinct parallel planes, resulting in a topological transition in one case and no transition in the other case This suggests that the impact of dissipation on the topological phase of a Weyl material can be qualitatively deduced from geometrical or symmetry arguments and need not depend on the particular realization. We start by presenting these general arguments in detail and illustrate the most relevant results by considering a continuous plasmonic medium, with broken time-reversal or inversion symmetry, as a model system of dissipative Weyl materials for electromagnetic waves
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