Half-metallicity recently predicted in the zigzag-edge graphene nanoribbons (ZGNRs) and the hydrogenated carbon nanotubes (CNTs) enables fully spin-polarized electric currents, providing a basis for carbon-based spintronics. In both carbon systems, the half-metallicity arises from the edge-localized electron states under an electric field, lowering the critical electric field Dc for the half-metallicity being an issue in recent works on ZGNRs. A properly chosen direction of the electric field alone has been predicted to significantly reduce Dc in the hydrogenated CNTs, which in this work turned out to be the case in narrow bilayer ZGNRs (biZGNRs). Here, our simple model based on the electrostatic potential difference between the edges predicts that for wide biZGNRs of width greater than ~2.0 nm (10 zigzag carbon chains), only one layer of the biZGNRs becomes half-metallic leaving the other layer insulating as confirmed by our density functional theory (DFT) calculations. The electric field-induced switching of the spin-polarized current path is believed to open a new route to graphene-based spintronics applications.
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