Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

TL;DR

This paper investigates how moderate Coulomb interactions can induce excitonic gaps in two-dimensional semi-Dirac semimetals, potentially leading to an excitonic insulator phase, and analyzes associated non-Fermi liquid behaviors.

Contribution

It demonstrates that Coulomb interactions can generate excitonic gaps in semi-Dirac semimetals and identifies TiO₂/VO₂ nanostructures as promising candidates for realization.

Findings

Moderately strong Coulomb interaction induces excitonic pairing.

Short-range couplings promote excitonic gap formation.

Semi-Dirac fermions exhibit non-Fermi liquid behavior at criticality.

Abstract

A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that TiO$_{2}$/VO$_{2}$ nanostructure provides a promising candidate for the realization of excitonic insulator. We also apply the renormalziation group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.