  We discuss the spectral properties of three-dimensional Dirac operators with
critical combinations of electrostatic and Lorentz scalar shell interactions
supported by a compact smooth surface. It turns out that the criticality of the
interaction may result in a new interval of essential spectrum. The position
and the length of the interval are explicitly controlled by the coupling
constants and the principal curvatures of the surface. This effect is
completely new compared to lower dimensional critical situations or special
geometries considered up to now, in which only a single new point in the
essential spectrum was observed.
