  Embedded eigenstates are nonradiative modes of an open structure with
momentum compatible with radiation, yet characterized by unboundedly large
Q-factors. Traditionally, these states originate from total destructive
interference of radiation from two or more non-orthogonal modes in periodic
structures. In this work, we demonstrate a novel class of embedded eigenstates
based on Berreman modes in epsilon-near-zero (ENZ) layered materials and
propose realistic silicon carbide (SiC) structures supporting high-Q (~10^3)
resonances based on these principles. The proposed structures demonstrate
strong absorption in a narrow spectral and angular range, giving rise to
quasi-coherent and highly directive thermal emission.
