  Bound states in the continuum (BICs) enable unique features in tailoring
light-matter interaction on nanoscale. These radiationless localized states
drive theoretically infinite quality factors and lifetimes for modern
nanophotonics, making room for a variety of emerging applications. Here we, for
the first time, pave a way from the recent developments in non-Hermitian
photonics and peculiar properties possessed by the so-called
$\mathcal{PT}$-symmetric optical structures to novel mechanism for the
quasi-BIC manifestation governed by the $\mathcal{PT}$-symmetry breaking. In
particular, we study regularities of the spontaneous $\mathcal{PT}$-symmetry
breaking in trilayer structures with the outer loss and gain layers consisting
of materials with permittivity close to zero. We reveal singular points on the
curves separating $\mathcal{PT}$-symmetric and broken-$\mathcal{PT}$-symmetry
states in the parametric space of the light frequency and the angle of
incidence. These singularities remarkably coincide with the BIC positions at
the frequency of volume plasmon excitation, where the dielectric permittivity
vanishes. The loss and gain value acts as an asymmetry parameter that disturbs
conditions of the ideal BIC inducing the quasi-BIC. Fascinating properties of
these quasi-BICs having ultrahigh quality factors and almost perfect
transmission can be utilized in sensing, nonlinear optics, and other
applications.
