Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions

We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and Newtonian dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO${}_2$/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, $Z\propto (\mathrm{\mid }\log E\mathrm{\mid }{)}^{-b}$ with universal $b = 3/2$.