Disordered and interacting parabolic semimetals in two and three dimensions

TL;DR

This paper investigates the stability of parabolic semimetals against disorder and interactions in two and three dimensions, revealing competing phases and potential quantum critical points relevant to materials like bilayer graphene.

Contribution

It provides a perturbative renormalization group analysis of disorder and Coulomb interactions in parabolic semimetals, highlighting the competition between broken symmetry states and disorder-driven phases.

Findings

Weak disorder induces Anderson insulator or diffusive metal in 2D and 3D.

Coulomb interaction leads to excitonic instability in clean systems.

Competition between broken symmetry and disorder-controlled phases is identified.

Abstract

A clean noninteracting parabolic semimetal is characterized by quadratic band touching between the conduction and the valence bands at isolated diabolic points in the Brillouin zone and describes a fermionic quantum critical system with dynamic exponent z=2. We consider the stability of such a semimetal against electronic interaction and quenched disorder using a perturbative renormalization group analysis for two and three spatial dimensions. For the noninteracting problem infinitesimally weak disorder leads to an Anderson insulator and a diffusive metal respectively in two and three dimensions. On the other hand, the long range Coulomb interaction causes an excitonic instability for the clean interacting problem towards a broken symmetry ground state in both dimensions. Our weak coupling analysis of the combined effects of disorder and interaction suggests the competition between a broken symmetry and a disorder controlled metallic or insulating states, but is inadequate for describing the quantum phase transitions among them. We discuss the relevance of our results for bilayer graphene and some 227 iridate compounds, and identify these materials as promising candidates for exploring novel disorder and interaction controlled quantum critical phenomena.