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

TL;DR

This paper investigates how Coulomb interactions induce non-Fermi liquid behavior at the quantum critical point of a topological phase transition in two-dimensional systems with anisotropic Weyl fermions, revealing a wide frequency range of non-Fermi liquid states.

Contribution

It demonstrates the emergence of interaction-driven non-Fermi liquid and marginal Fermi liquid behaviors in 2D Weyl fermions with anisotropic dispersion at a quantum critical point, using RG and large-N methods.

Findings

Non-Fermi liquid behavior with quasiparticle residue Z ∝ E^a for some a > 0

Marginal Fermi liquid behavior with Z ∝ (|log E|)^{-3/2} at low energies

Interaction effects lead to anomalous dimensions in fermionic dispersion parameters

Abstract

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, $Z \propto (|\log E|)^{-b}$ with universal $b = 3/2$.