具有圖形排列吸附原子石墨烯結構的量子自旋霍爾效應

Abstract

量子自旋霍爾效應最先被Kane和Mele預測在石墨烯結構中可以觀測到，然而由於碳原子產生的自旋軌道耦合效應相當微小，以至於無法得到可被實驗觀測的能帶間隙。我們研究覆蓋在石墨烯上的晶格狀排列吸附原子所產生的自旋軌道效應，更明確地說，我們研究邊緣態、其物理上的本質與邊緣態受電壓調控的能力。這樣的圖形排列吸附原子石墨烯結構成功地在Γ點上打開可被觀測的能帶間隙，且沿著扶手椅型石墨烯的邊上可發現邊緣態。這些邊緣態是屬於量子自旋霍爾效應的量子態，它們的自旋方向與群速度方向有著對掌性(chiral)的關係。這些邊緣態空間分布剖面圖容易受晶格狀排列吸附原子對稱或不對稱分布的影響。對稱分布的圖形排列吸附原子石墨烯結構，其邊緣態是「等比重混合類型(equal-weighting type)」，若是不對稱分布，其邊緣態則是「自旋極化類型(spin-polarized type)」，而所謂「等比種混合類型」邊緣態是指位在不同側邊界且帶有不同自旋方向的兩個類邊緣態(edge-state-like)波函數以等比重疊加。最值得關注的是我們證明可藉由電控方式(邊界電壓)來轉換邊緣態的混合類型。這些結果使我們能夠提出邊界轉換元件(edge-switching device)來轉換入射的自旋電子束(spin injection beam)。

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.