The magnetic $Z_2$ topological insulator on the AA-stacked bilayer graphene

TL;DR

This paper investigates the $Z_2$ topological insulator phase in AA-stacked bilayer graphene at van Hove singularities, revealing a novel topological state characterized by antiferromagnetic spin-density waves and quantum spin Hall features.

Contribution

It introduces a new $Z_2$ topological insulator phase in bilayer graphene with unique antiferromagnetic SDWs and topological properties distinct from monolayer systems.

Findings

Presence of antiferromagnetic spin-density waves in bilayer graphene.

Emergence of a nontrivial $Z_2$ topological invariant.

Alignment with quantum spin Hall effect characteristics.

Abstract

The properties displayed by graphene at van Hove singularities (VHS) have caught significant attention in recent years. The emergence of exotic quantum states at these singularities prompts investigations on their evolution within the realm of multilayer stacking structures. In our research, we delve into the study of a repulsive Hubbard model focusing on the AA-stacked bilayer graphene at VHS. Within the system's ground state, each of the top and bottom layers hosts a set of spin-density waves (SDWs). These SDWs each takes on three mutually perpendicular spin polarization directions. Importantly, there is noteworthy feature that their spin polarization directions in the two layers exist as elegant embodiments of antiferromagnetic arrangement, persvading the structure with a striking pattern. Referred to in prior research as the chiral SDWs, this intralayer density wave structure confers the system the characteristics of a Chern topological insulator. However, what is particularly fascinating is the pure divergence of the bilayer structure's topological traits when compared to its monolayer counterpart. The system exhibits a profound symmetry known as $Z_2$, preserving its invariance under the combined operations of time-reversal and interlayer exchange. Consequentely, the system's ground state manifests a seemingly trivial Chern number, yet harbors a profound and intricate nontrivial $Z_2$ topological invariant. These remarkable observations align our findings with the conceptual framework of the quantum spin Hall effect.