  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 use
the peculiar properties possessed by the so-called $\mathcal{PT}$-symmetric
optical structures to propose the 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.
