New quantum critical points of $j=3/2$ Dirac electrons in antiperovskite topological crystalline insulators

TL;DR

This paper investigates the effects of Coulomb interactions on $j=3/2$ Dirac electrons in cubic antiperovskite topological crystalline insulators, revealing new stable fixed points with specific symmetries that challenge emergent Lorentz invariance in solids.

Contribution

It identifies and characterizes three fixed points under Coulomb interactions, including a novel stable $O_h$-invariant fixed point with finite velocity anisotropy.

Findings

Stable $O_h$-invariant fixed point with finite velocity anisotropy.

Existence of Lorentz- and $O_h$-invariant fixed points.

Counterexample to emergent Lorentz invariance in solids.

Abstract

We study the effect of the long-range Coulomb interaction in $j=3/2$ Dirac electrons in cubic crystals with the $O_h$ symmetry, which serves as an effective model for antiperovskite topological crystalline insulators. The renormalization group analysis reveals three fixed points that are Lorentz invariant, rotationally invariant, and $O_h$ invariant. Among them, the Lorentz- and $O_h$-invariant fixed points are stable in the low-energy limit while the rotationally invariant fixed point is unstable. The existence of a stable $O_h$-invariant fixed point of Dirac fermions with finite velocity anisotropy presents an interesting counterexample to emergent Lorentz invariance in solids.