Note on "Quantum superconducting criticality in graphene and topological insulators"

TL;DR

This paper revises previous findings on the quantum critical point in 2D Dirac fermion systems, establishing a new critical flavor number for continuous superconducting transitions using an epsilon expansion.

Contribution

It provides a corrected calculation of the critical number of fermion flavors needed for a continuous transition in Dirac systems, refining earlier results with a leading order epsilon expansion.

Findings

Critical fermion flavor number is greater than 18.2699 for continuous transition.

For fermion flavors ≥ 0.5, the bosonic flavor threshold is lower than previously estimated.

Revised critical parameters impact understanding of quantum criticality in Dirac materials.

Abstract

We correct our previous conclusion regarding the fate of a charged quantum critical point across the superconducting transition for two dimensional massless Dirac fermion. Within the leading order $\epsilon$ expansion, we now find that the requisite number of four-component Dirac fermion flavors ($N_f$) for the continuous phase transition through a charged critical point is $N_f>18.2699$. For $N_f\geq1/2$, the critical number of bosonic flavors for this transition is significantly reduced as compared to the value determined in the absence of the Dirac fermions in the theory.