Topological quantum critical point in a triple-Weyl semimetal: non-Fermi-liquid behaviors and instabilities

TL;DR

This paper investigates the quantum critical point in a triple-Weyl semimetal, revealing non-Fermi-liquid behaviors and potential instabilities, including first-order transitions and nematic phases, driven by Coulomb interactions.

Contribution

It introduces a detailed analysis of the topological quantum critical point in triple-Weyl semimetals, highlighting the role of Coulomb interactions and resulting non-Fermi-liquid behaviors.

Findings

Coulomb interaction is marginal and induces an infrared fixed point.

System exhibits non-Fermi-liquid behaviors at the critical point.

Instabilities lead to first-order transition or nematic phase depending on fermion flavor.

Abstract

We study the quantum critical phenomena emerging at the transition from triple-Weyl semimetal to band insulator, which is a topological phase transition described by the change of topological invariant. The critical point realizes a new type of semimetal state in which the fermion dispersion is cubic along two directions and quadratic along the third. Our renormalization group analysis reveals that, the Coulomb interaction is marginal at low energies and even arbitrarily weak Coulomb interaction suffices to induce an infrared fixed point. We compute a number of observable quantities, and show that they all exhibit non-Fermi liquid behaviors at the fixed point. When the interplay between the Coulomb and short-range four-fermion interactions is considered, the system becomes unstable below a finite energy scale. The system undergoes a first-order topological transition when the fermion flavor $N$ is small, and enters into a nematic phase if $N$ is large enough. Non-Fermi liquid behaviors are hidden by the instability at low temperatures, but can still be observed at higher temperatures. Experimental detection of the predicted phenomena is discussed.