Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles

TL;DR

This study uses first principles calculations to reveal magnetic and charge density wave instabilities in rhombohedral multilayer graphene, showing how spin polarization opens a gap and how doping affects this magnetic gap.

Contribution

It demonstrates the magnetic gap opening mechanism in multilayer graphene using hybrid functionals and compares theoretical results with experimental data.

Findings

Magnetic gap of 38.6 meV in trilayer graphene with hybrid functionals

Spin polarization stabilizes an antiferromagnetic state

Doping closes the magnetic gap at high electron densities

Abstract

We investigate the occurrence of magnetic and charge density wave instabilities in rhombohedral-stacked multilayer (three to eight layers) graphene by first principles calculations including exact exchange. Neglecting spin-polarization, an extremely flat surface band centered at the special point ${\bf K}$ of the Brillouin zone occurs at the Fermi level. Spin polarization opens a gap in the surface state by stabilizing an antiferromagnetic state. The top and the bottom surface layers are weakly ferrimagnetic in-plane (net magnetization smaller than $10^{-3}\mu_B$), and are antiferromagnetic coupled to each other. This coupling is propagated by the out-of-plane antiferromagnetic coupling between the nearest neighbors. The gap is very small in a spin-polarized generalized gradient approximation, while it is proportional to the amount of exact exchange in hybrid functionals. For trilayer rhombohedral graphene it is $38.6$ meV in PBE0, in agreement with the $42$ meV gap found in experiments. We study the temperature and doping dependence of the magnetic gap. At electron doping of $n \sim 7 \times 10^{11}$ cm$^{-2}$ the gap closes. Charge density wave instabilities with $\sqrt{3}\times\sqrt{3}$ periodicity do not occur.