Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

TL;DR

This paper investigates the competition between density waves and quantum multicritical behavior in Dirac materials like graphene, using a functional renormalization group approach to analyze fixed points and phase transitions.

Contribution

It introduces a detailed analysis of multicritical points in Dirac materials with multiple order parameters using the Gross-Neveu-Yukawa model and reveals new fixed points depending on the number of Dirac fermions.

Findings

Stable fixed points depend on the number of Dirac fermions Nf.

Graphene (Nf=2) lacks a stable fixed point, indicating a first-order transition.

At large Nf, a new fixed point with coupled sectors becomes stable.

Abstract

We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions $N_f$. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order $\epsilon$ expansion. For small $N_f$, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large $N_f$, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate $N_f$, including the graphene case ($N_f = 2$) no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.