| Summary: | 碩士 === 國立交通大學 === 電子物理系所 === 105 === In this work, we consider induced localized states that are found out of a long metal gate that orients along an armchair atomic chain in a 2D graphene sheet. Specifically, we explore the topological nature of this gate-induced 1D energy branch. In contrast to the Tamm states in semiconductor surfaces, the gate-induced 1D branch does not require a threshold value for the gate-bias voltage V0. Two perspectives are taken to demonstrate the topological nature. First, we show that the boundary condition for the formation of the 1D branch can be cast into a rotation operator D that aims to rotate the'K -valley pseudospinχp-1 the to the K -valley pseudospin χp1 , for a given longitudinal wave vector ky , and at the right energy. We have shown, for a given ky and V0, that the angle between the pseudospins χp1 and χp-1 varies over 2π as the energy scans across the energy gap. Equally importantly, we show that as long as V0 is nonzero, the rotation axis of D is perpendicular to the plane formed by χp1 and χp−1 . This show that the 1D branch boundary condition must be satisfied for any ky and finite V0 values. As such, the branch will touch upon the Dirac point, where ky=0. Second, we look at the real space pseudospin orientation as ky varies over its Brillouin zone. Discontinuous in the pseudospin orientation angle φχ across the Dirac point is obtained. This is a signature of the topological nature of the 1D branch, similar but not exactly the same as that discussed in Hatsugai’s (PRL 2002) [1] and Montambaux’s (PRB 2011) [2]. Base on this two perspectives we have demonstrate the topological nature of the gate-induced 1D branch.
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