Mott multicriticality of Dirac electrons in graphene

TL;DR

This paper investigates the complex phase transitions in graphene's honeycomb lattice, focusing on the interplay of antiferromagnetic and density order parameters using a theoretical framework, revealing multicritical behaviors and phase diagram structures.

Contribution

It introduces a study of multicritical behavior in graphene using the Gross-Neveu-Yukawa theory with two coupled order parameters, highlighting the conditions for different phase transition types.

Findings

Phase diagram shows tetracritical structure for N_f=2.

Coupling of order parameters induces multicritical behavior.

Transition nature depends on fermion flavor number and dimensionality.

Abstract

We study the multicritical behavior for the semimetal-insulator transitions on graphene's honeycomb lattice using the Gross-Neveu-Yukawa effective theory with two order parameters: the SO(3) (Heisenberg) order parameter describes the antiferromagnetic transition, and the $\mathbb{Z}_2$ (Ising) order parameter describes the transition to a staggered density state. Their coupling induces multicritical behavior which determines the structure of the phase diagram close to the multicritical point. Depending on the number of fermion flavors $N_f$ and working in the perturbative regime in vicinity of three (spatial) dimensions, we observe first order or continuous phase transitions at the multicritical point. For the graphene case of $N_f=2$ and within our low order approximation, the phase diagram displays a tetracritical structure.