Quantum critical points of j= 32 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 Oh 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 Oh invariant. Among them, the Lorentz- and Oh-invariant fixed points are stable in the low-energy limit, while the rotationally invariant fixed point is unstable. The existence of a stable Oh-invariant fixed point of Dirac fermions with finite velocity anisotropy presents an interesting counterexample to emergent Lorentz invariance in solids.