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

摘要

We study the effects of Coulomb interaction between 2D Weyl fermions withanisotropic dispersion which displays relativistic dynamics along one directionand Newtonian dynamics along the other. Such a dispersion can be realized inphosphorene under electric field or strain, in TiO$_2$/VO$_2$ superlattices,and, more generally, at the quantum critical point between a nodal semimetaland an insulator in systems with a chiral symmetry. Using the one-looprenormalization group approach in combination with the large-$N$ expansion, wefind that the system displays interaction-driven non-Fermi liquid behavior in awide range of intermediate frequencies and marginal Fermi liquid behavior atthe smallest frequencies. In the non-Fermi liquid regime, the quasiparticleresidue $Z$ at energy $E$ scales as $Z \propto E^a$ with $a >0$, and theparameters of the fermionic dispersion acquire anomalous dimensions. In themarginal Fermi-liquid regime, $Z \propto (|\log E|)^{-b}$ with universal $b =3/2$.