| Summary: | 碩士 === 國立交通大學 === 電子物理系所 === 103 === The quantum spin Hall state was first predicted in graphene by Kane and Mele, although the gap is unobservably small due to carbon’s weak spin-orbit coupling. We investigate the spin-orbit effects due to an adatom lattice on a graphene sheet. More specifically, we study the edge states, and their physical nature, and the electric gate-tunning capabilities of these edge states. Such an adatom-patterned graphene sheet has a gap opening at the Γ point. Cutting into the form of a ribbon along the armchair edge, edge states are obtained. These states are of the quantum spin-Hall-type, namely that they are chiral with a definite relation between their spin and group velocity directions. The spatial profile of these edge-states are shown to be sensitive to the symmetric or asymmetric positioning of the adatom lattice on the armchair graphene nanoribbon (AGNR). The edge-states are of either an equal-weighting type or a spin-polarized type for, respectively, the symmetric and asymmetric adatom-patterned AGNRs. The equal-weighting type edge-states are equal-weight superposition of two edge-state-like wave functions localized at opposite AGNR edges and with opposite spin directions. Most interestingly, we have demonstrated switching of the edge-states from one type to another type by electrical means: via an edge-potential. This allows us to propose a edge-switching device for a given spin injection beam.
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