  We investigate linear and nonlinear spectral singularities in the transverse
electric and transverse magnetic modes of a slab laser consisting of an active
planar slab sandwiched between a pair of Graphene or Weyl semimetal thin
sheets. The requirement of the presence of linear spectral singularities gives
the laser threshold condition while the existence of nonlinear spectral
singularities due to an induced weak Kerr nonlinearity allows for computing the
laser output intensity in the vicinity of the threshold. The presence of the
Graphene and Weyl semimetal sheets introduces additional physical parameters
that we can use to tune the output intensity of the laser. We provide a
comprehensive study of this phenomenon and report peculiarities of lasing in
the TM modes of the slab with Weyl semimetal coatings. In particular, we reveal
the existence of a critical angle such that no lasing seems possible for TM
modes of the slab with smaller emission angle. Our results suggest that for TM
modes with emission angle slightly exceeding the critical angle, the laser
output intensity becomes highly sensitive to the physical parameters of the
coating.
