  Two-dimensional Dirac semimetal with tilted Dirac cone has recently attracted
increasing interest. Tilt of Dirac cone can be realized in a number of
materials, including deformed graphene, surface state of topological
crystalline insulator, and certain organic compound. We study how Dirac cone
tilting affects the low-energy properties by presenting a renormalization group
analysis of the Coulomb interaction and quenched disorder. Random scalar
potential or random vector potential along the tilting direction cannot exist
on its own as it always dynamically generates a new type of disorder, which
dominates at low energies and turns the system into a compressible diffusive
metal. Consequently, the fermions acquire a finite disorder scattering rate.
Moreover, the isolated band-touching point is replaced by a bulk Fermi arc in
the Brillouin zone. These results are not qualitatively changed when the
Coulomb interaction is incorporated. In comparison, random mass and random
vector potential along the non-tilting direction can exist individually,
without generating other types of disorder. They both suppress tilt at low
energies, and do not produce bulk Fermi arc. Upon taking the Coulomb
interaction into account, the system enters into a stable quantum critical
state, in which the fermion field acquires a finite anomalous dimension but the
dynamical exponent $z=1$. These results indicate that Dirac cone tilt does lead
to some qualitatively different low-energy properties comparing to the untilted
system.
