Dirac points embedded in the continuum

Hermitian Dirac points play a fundamental role in topological phenomena. The introduction of gain or loss leads to non-Hermitian systems, where Dirac points transform into pairs of exceptional points connected by a Fermi arc. Open non-Hermitian systems also manifest bound states in the continuum (BICs), which are nonradiating resonances located within the band of radiation states. So far, exceptional points have been shown to be robust when interacting with BICs. However, our work unveils that the intersection of two BICs from distinct energy bands along the Fermi arc can prevent the formation of exceptional points, restoring a genuine Hermitian Dirac point instead, albeit surrounded by non-Hermitian states. This represents a different mechanism for the formation of Dirac points embedded in the continuum of radiation, which combines the physics associated to Dirac points and the resonant properties of BICs in non-Hermitian systems. The concept is analyzed using a general model and further explored in a waveguiding photonic system based on hyperbolic dispersion media.