Environmental Breakdown of Topological Interface States in Armchair Graphene Nanoribbon Heterostructures: Is it true?

Abstract

We investigate the environmental stability of topological interface states (IFs) in two sandwich nanostructures, BNNR/AGNRH/BNNR and BNNR/AGNRH/NBNR, where AGNRH denotes an armchair graphene nanoribbon heterostructure and BNNR (NBNR) represents a boron nitride nanoribbon. The former corresponds to a same-topology configuration, whereas the latter realizes a reverse-topology configuration. Using a bulk boundary perturbation approach, we show that in BNNR/AGNRH/BNNR the IFs are destroyed by chirality breaking induced by symmetric BN environments at both interfaces. In contrast, the IFs in the reverse-topology structure remain robust against lateral interface interactions from BN atoms. Transport calculations further demonstrate that the surviving IFs in BNNR/AGNRH/NBNR exhibit the characteristic behavior of topological double quantum dots, with an enhanced interdot hopping strength compared with vacuum boundary conditions. These results reveal that BN environments can either suppress or reinforce topological interface states, depending critically on the topology of the surrounding nanoribbons.

Figures (5)

• Figure 1: Schematic illustration of an armchair graphene nanoribbon heterostructure (AGNRH) laterally embedded in a hexagonal boron nitride (BN) sheet, forming two distinct configurations: (a) a same-topology structure, 2-BNNR/9-7-9-AGNRH/2-BNNR, and (b) a reverse-topology structure, 2-BNNR/9-7-9-AGNRH/2-NBNR. White and blue sites denote boron and nitrogen atoms, respectively. $R_1$ and $R_2$ represent the unit cells (u.c.) of the 9-AGNR/2-BN and 7-AGNR/3-BN junctions, respectively. The tunable parameter $t_{in}$ characterizes the interfacial coupling between the AGNRH and the BNNRs. The symbols $\Gamma_{L}$ ($\Gamma_{R}$) represent the electron tunneling rates between the left (right) electrode and the leftmost (rightmost) atoms at the zigzag edges.
• Figure 2: Quasi-1D electronic band structures of AGNRs embedded in hexagonal BN sheets. Same-topology configurations: (a) 4-BNNR/7-AGNR/4-BNNR and (b) 4-BNNR/9-AGNR/4-BNNR. Inverse-topology configurations: (c) 4-BNNR/7-AGNR/4-NBNR and (d) 4-BNNR/9-AGNR/4-NBNR. We have adopted $t_{in}=2.7$ eV and $\Delta = 2.7$ eV. $L$ is the length of $R_1$ unit cell.
• Figure 3: Energy spectra of finite AGNR (AGNRH) segments as functions of interfacial hopping $t_{in}$ at $\Delta = 2.7$ eV. Same-topology scenario: (a) 4-BNNR/7-AGNR/4-BNNR and (b) 4-BNNR/9-7-9-AGNRH/4-BNNR. Inverse-topology scenario: (c) 4-BNNR/7-AGNR/4-NBNR and (d) 4-BNNR/9-7-9-AGNRH/4-NBNR.
• Figure 4: Charge densities of the interface state $\Sigma_{IF,C}$ in $9_{10}-7_8-9_{10}$-AGNRH embedded in BN at $\Delta = 2.7$ eV. (a)-(c) Inverse-topology: $t_{in}=0$ ($\Sigma_{IF,C}=7.53$ meV), $t_{in}=0.2~t$ ($\Sigma_{IF,C}=8.81$ meV), $t_{in}=0.8~t$ ($\Sigma_{IF,C}=50.96$ meV). (d)-(f) Same-topology: $t_{in}=0.2~t$ ($\Sigma_{IF,C}=31.35$ meV), $t_{in}=0.4~t$ ($\Sigma_{IF,C}=117.57$ meV), $t_{in}=0.8~t$ ($\Sigma_{IF,C}=0.402$ eV).
• Figure 5: Transmission coefficients ${\cal T}_{GNR}(\varepsilon)$ of the 4-BNNR/$9_6-7_8-9_6$-AGNRH/4-NBNR structure for various $t_{in}$ at $\Gamma_t = 2.7$ eV. (a) $t_{in} = 0.6~t$, (b) $t_{in} = 0.7~t$, (c) $t_{in} = 0.8~t$, and (d) $t_{in} = 0.9~t$.