Quantum critical points of j=3/2 Dirac electrons in antiperovskite topological crystalline insulators

Abstract

We study the effect of the long-range Coulomb interaction in j=3/2 Dirac electrons in cubic crystals with the O[subscript 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[subscript h] invariant. Among them, the Lorentz- and O[subscript 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[subscript h]-invariant fixed point of Dirac fermions with finite velocity anisotropy presents an interesting counterexample to emergent Lorentz invariance in solids.