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Weyl fermions with tilted linear dispersions characterized by severaldifferent velocities appear in some systems including the quasi-two-dimensionalorganic semiconductor $\alpha$-(BEDT-TTF)$_2$I$_3$ and three-dimensionalWTe$_2$. The Coulomb interaction between electrons modifies the velocities inan essential way in the low-energy limit, where the logarithmic correctionsdominate. Taking into account the coupling to both the transverse andlongitudinal electromagnetic fields, we derive the renormalization groupequations for the velocities of the tilted Weyl fermions in two dimensions, andfound that they increase as the energy decreases and eventually hit the speedof light $c$ to result in the Cherenkov radiation. Especially, the systemrestores the isotropic Weyl cone even when the bare Weyl cone is stronglytilted and the velocity of electrons becomes negative in certain directions.

Coulomb interaction effect in tilted Weyl fermion in two dimensions