Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions

TL;DR

This paper investigates a novel anisotropic non-Fermi liquid quantum criticality emerging at topological phase transitions between double-Weyl semimetals and insulators, revealing unique electronic behaviors in three dimensions.

Contribution

It introduces a new class of quantum criticality characterized by anisotropic non-Fermi liquid behavior at topological phase transitions, supported by renormalization group analysis.

Findings

Anisotropic renormalization of Coulomb interaction

Emergence of strongly correlated electronic excitations

Predictions for observable effects in candidate materials

Abstract

Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excitation in three spatial dimensions. Using the standard renormalization group methods, large $N_f$ theory and the $\epsilon= 4-d$ method with fermion flavor number $N_f$ and spatial dimension $d$, we obtain the anomalous dimensions of electrons ($\eta_f=0.366/N_f $) in large $N_f$ theory and the associated anisotropic scaling relations of various physical observables. Our results may be observed in candidate materials for DWSMs such as HgCr$_2$Se$_4$ or SrSi$_2$ when the system undergoes a TQPT.