Abstract
We show that the spontaneous magnetization is formed at the zigzag boundary between monolayer and bilayer graphene by the self-consistent calculation based on Hubbard model. In a monolayer- bilayer graphene superlattice with zigzag boundaries, it is surprising that nearly 100% spin polarization is achieved in the energy window around the Dirac point, no matter the magnetization configuration at two boundaries is parallel or antiparallel. The reason is that the low-energy transport is only influenced by the magnetization at one edge, but not by that at the other. The underlying physics is unveiled by the spin-split band structure and the distribution of the wave-function pertaining to the lowest (highest) subband of electron (hole).
Highlights
We assume that the edge atoms at ZMBGBs are terminated by hydrogen atoms so that the edge magnetization is totally contributed by the edge-localized π-orbital state which is well described by the Hubbard model
Since the edge magnetizations are confirmed at ZMBGBs in MBGS, we discuss the consequence in the spin-polarized transport
We focus on the energy window [− Δ, Δ ]
Summary
The length of a period is L p = Lm + Lb. In our work, we have not considered possible reconstructions of ZMBGBs. And we assume that the edge atoms at ZMBGBs are terminated by hydrogen atoms so that the edge magnetization is totally contributed by the edge-localized π-orbital state which is well described by the Hubbard model. We consider that system is translational invariant along the y direction For such a MBGS, the Hamiltonian can be reduced to a matrix with finite dimension describing a supercell for given longitudinal and transversal Bloch wave-vectors kx, ky. Where HDσ is the Hamiltonian of the device region, and the retarded self-energy ΣrLσ (Rσ) due to the coupling to the terminal L(R) can be calculated numerically.
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