Fermion-induced quantum critical points (FIQCPs) were recently discovered at the putatively first-order transitions between two-dimensional (2D) Dirac semimetals and the Kekule valence bond solids on the honeycomb lattice by sign-free quantum Monte Carlo simulations [Nat. Commun. 8, 314 (2017)]. Here, we investigate possible FIQCPs in 3D topological Weyl semimetals at a $Z_3$ symmetry-breaking transition that is putatively first-order according to the Landau criterion. We construct a lattice model featuring 3D double-Weyl fermions (monopole charges $\pm 2$), and we show that $Z_3$ nodal-nematic transitions occur under finite Hubbard interaction. Furthermore, using renormalization-group analysis, we identify such a transition as a genuine FIQCP where the cubic terms are irrelevant and an enlarged U(1) symmetry emerges at low energy. We further discuss quantum critical behaviors and experimental signatures of such FIQCPs in 3D double-Weyl semimetals.

• Received 23 September 2016
• Revised 21 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.155112