Abstract
Analytic solutions of the quasi-one-dimensional (q1D) electron states around an extended line defect in a graphene lattice are derived within the tight-binding model. Then, the electronic properties of this kind of boundary state in graphene are studied in detail. It is found that one subband composed of the even-parity boundary states emerges in the vicinity of the Dirac point. In particular, when the bulk band is gapped, such a one-dimensional subband remains in the bandgap, spanning two inequivalent valleys. In addition, this boundary state subband exhibits nontrivial dispersion, which can carry the valley polarized charge current flowing along the extended line defect. As a result, the line defect behaves like a one-dimensional channel for electronic transport. Moreover, its appearance in graphene or a hexagonal boron nitride sheet provides a promising way to print electric circuits in these two-dimensional materials.
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