Canted antiferromagnetism and excitonic order in gated double-layer graphene

Abstract

We study the effects of the electron-electron interactions on the excitonic properties and charge-density modulations in the AB stacked double-layer (DL) graphene, placed in the external gate-potential $V$. The coexistence of the canted antiferromagnetic order and excitonic pairing gap has been studied with the help of the generalized Hubbard model. We calculate the chemical potential $μ$, the average charge density difference between the layers $δ{\bar{n}}$, the antiferromagnetic gap-function $Δ_{\rm AFM}$ and the excitonic order parameters $Δ_σ$ in the zero temperature limit. We found that the excitonic pairing order parameter has a larger energy scale than the canted antiferromagnetic gap-function. The charge neutrality, in the DL graphene system, occurs only in the absence of the external gate-potential $V$. Moreover, we have shown that the values of the antiferromagnetic gap-function $Δ_{\rm AFM}$ and excitonic order parameter $Δ_σ$ are always increasing at the large values of inter-layer Coulomb interaction, while they are decreasing for large values of the applied gate-potential $V$.

Figures (5)

• Figure 1: (Color online) The structure of the AB double-layer (DL) graphene in the external electric field potential $V$. The layers of the system have been indicated as $\ell=1$ (the bottom layer) and $\ell=2$ (the upper layer). In the picture, the $A$, $\tilde{A}$ atomic sites are represented by the grey balls, and the $B$,$\tilde{B}$ atomic sites are represented by green balls.
• Figure 2: (Color online) The numerical results for $\mu$ (see panel (a)), $\Delta_{\uparrow}$ (see in panel (b)), as a function of the inter-layer Coulomb interaction parameter $W$. The calculations have been done in the zero temperature limit, and different values of the interaction parameter $U$ and inverse-filling coefficient $\kappa$ have been considered. The external gate-potential has been fixed at the value $V=\gamma_0=3$ eV.
• Figure 3: (Color online) The numerical results for $\Delta_{\rm AFM}$ (see in panel (a)) and $\delta{\bar{n}}$ (see in panel (b)) as a function of the inter-layer Coulomb interaction parameter $W$. The calculations have been done in the zero temperature limit, and different values of the interaction parameter $U$ and inverse-filling coefficient $\kappa$ have been considered. The external gate-potential has been fixed at the value $V=\gamma_0=3$ eV.
• Figure 4: (Color online) The numerical results for $\mu$ (see on panel (a)) and $\Delta_{\uparrow}$ (see on panel (b)), as a function of the gate-potential $V$. The calculations have been done in the zero temperature limit $T=0$. The Coulomb interaction parameter $U$, the inter-layer interaction $W$ and the inverse filling-coefficient $\kappa$ have been set respectively at the values $U=2\gamma_0$, $W=\gamma_0$ and $\kappa=0.8$.
• Figure 5: (Color online) The numerical results for $\Delta_{\rm AFM}$ (see on panel (a)) and $\delta{\bar{n}}$ (see on panel (b)), as a function of the gate-potential $V$. The calculations have been done in the zero temperature limit $T=0$. The Coulomb interaction parameter $U$, the inter-layer interaction $W$ and the inverse filling-coefficient $\kappa$ have been set respectively at the values $U=2\gamma_0$, $W=\gamma_0$ and $\kappa=0.8$.