Abstract
This chapter explores how the gate potential of Nc, the number of chains along the armchair direction (along the y-axis), in two-dimensional graphene can produce topological localized states (LSs). The wave functions of the LSs show strongly localized behavior around the gate and decay away from the gate. The number of LSs is shown to depend on the number of chains, Nc. It is remarkable that there is one branch and two branches of LSs launching from the Dirac cone for single-chain gate (Nc = 1) and multi-chain gate (Nc ≥ 2), respectively. Such topological LSs are formed as long as the gate-induced potential V0 is non-zero. The topological origin of the formation of LSs can be interpreted by the mechanism of pseudospin rotations, that is, the rotation upon a valley-dependent pseudospin is equivalent to another valley-dependent pseudospin. It is notable that both pseudospins are on the same side of the gate potential. The picture of pseudospin rotations can be extracted from the LS secular equation, which is derived based on the scattering process upon applying the gate potential to a graphene sheet. As the energy E varies across the entire energy gap for a given ky, the rotation angle of the pseudospin-rotation operator fits within the variation range of the relative angle ΔΘp between two pseudospins. These LS branches reveal a Dirac-point signature, with dispersion relations arising out of the Dirac point (at ky = 0). For general multiple (Nc > 1) chain potential cases, the number of LS branches, NLS, increases with the potential strength V0 up to a maximum of NLS, max = Nc. It is important that there are only two LS branches coupling to the Dirac-point signature in the case of Nc > 1.
Original language | English |
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Title of host publication | Rich Quasiparticle Properties in Layered Graphene-related Systems |
Publisher | World Scientific Publishing Co. |
Pages | 225-255 |
Number of pages | 31 |
ISBN (Electronic) | 9789811277795 |
ISBN (Print) | 9789811277788 |
DOIs | |
Publication status | Published - 2023 Jan 1 |
All Science Journal Classification (ASJC) codes
- General Biochemistry,Genetics and Molecular Biology
- General Engineering
- General Physics and Astronomy