We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in ${\mathrm{TiO}}_2/{\mathrm{VO}}_2$ superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-$N$ expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue $Z$ at energy $E$ scales as $Z\propto E^a$ with $a>0$, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, $Z\propto (|\log E|{)}^{-b}$ with universal $b=3/2$.

• Received 1 August 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.076803