Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators

TL;DR

This paper studies how long-range Coulomb interactions influence topological phase transitions in three-dimensional semi-metals, revealing that such interactions stabilize the transition and prevent relativistic behavior, with universal physical ratios derived.

Contribution

It demonstrates that Coulomb interactions do not destabilize topological transitions protected by chiral symmetry and shows they prevent the transition from being relativistic, introducing universal ratios.

Findings

Topological transition remains stable under Coulomb interactions.

Electron velocity exceeds chiral symmetry order parameter velocity.

Transition cannot be relativistic due to Coulomb effects.

Abstract

Topological states may be protected by a lattice symmetry in a class of topological semi-metals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space defines a chirality concretely, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include Dirac semi-metal (DSM) in a distorted spinel, BiZnSiO$_4$, protected by a mirror symmetry and DSM in Na$_3$Bi, protected by a rotational symmetry. In these states, topology and a chiral symmetry are intrinsically tied. In this work, we investigate characteristics interplay between a chiral symmetry order parameter and instantaneous long-range Coulomb interaction with the standard renormalization group method. We show that a topological transition associated with a chiral symmetry is stable under the presence of the Coulomb interaction and the electron velocity always becomes faster than one of a chiral symmetry order parameter. Thus, the transition {\it must not} be relativistic, which implies a supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. {Asymptotically exact} universal ratios of physical quantities such as energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.