  There is a close connection between various new phenomena in Weyl semimetals
and the existence of linear band crossings in the single particle description.
We show, by a full self-consistent mean-field calculation, how this picture is
modified in the presence of long-range Coulomb interactions. The chiral
symmetry breaking occurs at strong enough interactions and the internode
interband excitonic pairing channel is found to be significant, which
determines the gap-opened band profile varying with interaction strength.
Remarkably, in the resultant interacting phase, finite band Chern number jumps
in the three-dimensional momentum space are retained, indicating the robustness
of the topologically nontrivial features.
