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It is generally believed that topological insulators are highly immune to non-magnetic defects, but there is still a lack of verification at the mesoscopic scale of device applications. By using the first-principles calculations and scattering matrix methods, we take SiSnF2 monolayer ribbons as an illustration to study the effects of defects and sizes on the electron transport in topological insulators. First-principles calculations show that SiSnF2 transforms into a topological insulator under a tensile strain greater than 2%. The data of an effective tight-binding model was got by using a genetic algorithm to calculate the transport properties of the topological insulator SiSnF2 ribbons, and it was found that edge states can also be disrupted by random vacancy defects. The method for calculating local current is: $J_{a b}=i\left[\psi_b^{\dagger}\left(H_{a b}\right)^{\dagger} M \psi_a-\psi_a^{\dagger} M H_{a b} \psi_b\right]$ where $H_{a b}$ is the hopping matrix from lattice site b to lattice site a, $\psi_a\left(\psi_b\right)$ is the vector composed of the wave function components at lattice site a(b), $\psi_a^{\dagger}\left(\psi_b^{\dagger}\right)$ is the Hermitian conjugate of $\psi_a\left(\psi_b\right)$, and M is the density matrix.
For a ribbon with a length of 18.8 nm and a width of 8.2 nm, which containing thousands of atoms, when there are no defects, the local current is concentrated at the edge of the ribbon, and the conductance is the ideal value of the topological edge state, 2 e2/h. When the defect concentration is 1%, the transport calculations show that the edge current has been appreciably disturbed, but the backscattering is still effectively suppressed, and the current bypasses the defect and still goes forward. When the concentration is 5%, the edge electrons are scattered deep into the ribbon and are scattered with the opposite edge, destroying the topological edge state and reducing the conductance to 0.6 e2/h. Therefore, the transformation from topological to normal insulator caused by defects happens gradually instead of abruptly. The study found an obvious transport quantum size effect: increasing the ribbon width can reduce electron scattering between edges and enhance the stability of topological edge states; while increasing the length will increase electron localization and electron scattering between edges, reducing the stability of topological edge states.-
Keywords:
- topological insulators /
- electron transport /
- defects /
- quantum size effects
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