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

Instability and topological robustness of Weyl semimetals against Coulomb interaction