Applied electric and magnetic field effects on the bandgap formation and antiferromagnetic ordering in AA-stacked Bilayer Graphene

TL;DR

This work develops a double-layer Hubbard model for AA-stacked bilayer graphene under independent layer gating and a perpendicular magnetic field to study excitonic pairing, antiferromagnetic order, and bandgap formation. By performing a Hubbard-Stratonovich decoupling and solving self-consistent mean-field equations, the authors reveal rich phase behavior driven by layer voltages, interlayer Coulomb coupling $W$, intra- and interlayer Coulomb interactions $U$ and $W$, and the magnetic field, including large tunable bandgaps and spin-selective excitonic states. The results show how doping, gating, and magnetic field collectively enable transitions among excitonic insulator, semiconducting, and insulating regimes, with potential spintronic implications such as spin-valve-like control of excitons and Wigner localization under strong fields. The study highlights the tunable electronic structure of AA-BLG and points to experimental routes via pulsed electric fields and Wannier-Stark localization to realize large-gap graphene-based materials for optoelectronic and spintronic applications.

Abstract

In this study, we consider a two-layer graphene structure stacked in the AA form and exposed to the influence of two different electric fields applied to different layers. The graphene layers are also subjected to an external magnetic field perpendicular to the planes of the layers. We investigate the possible effects of the applied in-plane fields and the magnetic field on excitonic pairing, antiferromagnetic order, and the chemical potential. Simultaneously, we analyze the effects of the interlayer Coulomb interaction potential on the physical properties of the considered system. We demonstrate that the application of planar electric fields leads to the formation of an unusually large bandgap in the electronic band structure, which is not typical for AA-stacked bilayer graphene. We discuss various values of the applied electric field potentials and show their influence on the electronic band structure of the system. Additionally, we identify the existence of a critical value of the magnetic field above which Wigner crystallization-like effect is present for the electrons, also affecting the excitonic gap in one spin channel. The results obtained in this study could be important for applications of AA-stacked bilayer graphene as a large band-gap material.

Figures (15)

• Figure 1: The presented structure of the gated AA-stacked bilayer graphene (AA-BLG) system illustrates the application of electric field potentials $V_1$ and $V_2$ to the bottom layer ($\ell = 1$ ) and top layer ($\ell = 2$), respectively. The diagram highlights the positions of atoms corresponding to the different sublattices: $A_1$ and $B_1$ in the bottom layer, and $A_2$ and $B_2$ in the top layer. In the diagram, the intralayer hopping parameter $\gamma_0$ represents the hopping between atoms within the same layer, while the interlayer hopping parameter $\gamma_1$ describes the tunneling between atoms of adjacent layers. Additionally, the formation of excitons is depicted in brown, illustrating the coupling between particles on sublattice sites $A_1$ and $A_2$, as well as $B_1$ and $B_2$. This excitonic formation occurs due to the electronic correlations.
• Figure 2: The staggering antiferromagnetic ordering in the AA bilayer graphene system. The antiferroamgnetic order parameter is shown at each sublattice site position in the bilayer. The order parameter $\Delta_{\rm AFM}$ is defined in Eq.(\ref{['Equation_12']}).
• Figure 3: The numerical solutions for key physical quantities are presented as functions of the local Coulomb potential $U$. Specifically, the following results are illustrated: panel (a): chemical potential $\mu$, panel (b): Antiferromagnetic order parameter $\Delta_{\rm AFM}$, panel (c): average density imbalance functions $\delta \bar{n}_{1}$ and $\delta \bar{n}_{2}$, panel (d): Excitonic order parameters $\Delta_{\uparrow}$ and $\Delta_{\downarrow}$. The interlayer Coulomb potential is fixed at $W = 0.5 \gamma_0$, while the magnetic field parameter $\tilde{B}$ is set to $\tilde{B} = 0.2$. Additionally, the layer voltages are set to $V_1 = 0.2 \gamma_0$ and $V_2 = 0.5 \gamma_0$.
• Figure 4: The numerical solutions for key physical quantities are presented (in undoped AA bilayer graphene with $x=0.0$) as functions of the interlayer Coulomb potential $W$. Specifically, the following results are illustrated: panel (a): chemical potential $\mu$, panel (b): antiferromagnetic order parameter $\Delta_{\rm AFM}$, panel (c): average density imbalance functions $\delta \bar{n}_{1}$ and $\delta \bar{n}_{2}$, panel (d): excitonic order parameters $\Delta_{\uparrow}$ and $\Delta_{\downarrow}$. The intralayer Coulomb potential is fixed at $U = 3.3\gamma_0$, while the magnetic field parameter $\tilde{B}$ is set to $\tilde{B} = 0.2$. Additionally, the layer voltages are set to $V_1 = 0.2 \gamma_0=0.56$ eV and $V_2 = 0.5 \gamma_0=1.4$ eV.
• Figure 5: The numerical solutions for key physical quantities (in doped AA bilayer graphene: $x=1$) are presented as functions of the interlayer Coulomb potential $W$. Specifically, the following results are illustrated: panel (a): chemical potential $\mu$, panel (b): antiferromagnetic order parameter $\Delta_{\rm AFM}$, panel (c): average density imbalance functions $\delta \bar{n}_{1}$ and $\delta \bar{n}_{2}$, panel (d): excitonic order parameters $\Delta_{\uparrow}$ and $\Delta_{\downarrow}$. The intralayer Coulomb potential is fixed at $U = 3.3\gamma_0$, while the magnetic field parameter $\tilde{B}$ is set to $\tilde{B} = 0.2$. Additionally, the layer voltages are set to $V_1 = 0.2 \gamma_0=0.56$ eV and $V_2 = 0.5 \gamma_0=1.4$ eV.