Abstract
Weyl points are the simplest topologically-protected degeneracy in a three-dimensional dispersion relation. The realization of Weyl semimetals in photonic crystals has allowed these singularities and their consequences to be explored with electromagnetic waves. However, it is difficult to achieve nonlinearities in such systems. One promising approach is to use the strong-coupling of photons and excitons, because the resulting polaritons interact through their exciton component. Yet topological polaritons have only been realized in two dimensions. Here, we predict that the dispersion relation for polaritons in three dimensions, in a bulk semiconductor with an applied magnetic field, contains Weyl points and Weyl line nodes. We show that absorption converts these Weyl points to Weyl exceptional rings. We conclude that bulk semiconductors are a promising system in which to investigate topological photonics in three dimensions, and the effects of dissipation, gain, and nonlinearity.
Highlights
Degeneracies in band structures are a key concept at the heart of recent developments in condensed-matter physics and optics [1]
In the non-Hermitian case [4,5,10], with absorption, we show that the Weyl points become Weyl exceptional rings, which can be reached by tuning the frequency and the angle between the propagation direction and the applied field
Our primary interest is in the degeneracy structure of the magneto-exciton-polariton dispersion relation, which we first consider in the Hermitian case without dissipation
Summary
Degeneracies in band structures are a key concept at the heart of recent developments in condensed-matter physics and optics [1]. Such work is being extended to dissipative systems, such as photonic materials with gain and loss, described by non-Hermitian Hamiltonians [4] In this case the singularities include exceptional points [5,6] in parameter space, at which both the frequencies and lifetimes of the modes become degenerate. In the three-dimensional case, Weyl points can become Weyl exceptional rings [8], which have a quantized Chern number and a quantized Berry phase Like their counterparts in Hermitian systems, such non-Hermitian singularities give rise to interesting physical effects [9], including edge modes [10], unusual transmission properties, topological lasing, and Fermi arcs arising from half-integer topological charge [11]
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