  We study the interplay of the structural phase transition, flat electronic
band dispersion, and metal-to-insulator transition (MIT) in the parent
compounds of the Ru-pnictide superconductors by using first-principles
calculations. Our electron and phonon calculations reveal that Ru(P,As) undergo
MIT accompanied by orthorhombic to monoclinic distortion at low temperature,
but RuSb stays orthorhombic and metallic in agreement with the experimental
findings. We find that although small monoclinic distortion can remove the van
Hove singularity at the Fermi level, it does not immediately gap out the Fermi
surface and a large value of monoclinic distortion is necessary for a clear MIT
suggesting the possibility of an intermediate pseudogapped monoclinic metallic
phase. Furthermore, we predict a light-induced two-step insulator-to-metal and
structural transitions in the monoclinic phases of RuP and RuAs, which can be
tested in future ultrafast pump-probe experiments as an alternative ideal play
ground to VO$_2$.
