Electronic states and spin-filter effect in three-dimensional topological insulator Bi<sub>2</sub>Se<sub>3</sub> nanoribbons

Electronic states and spin-filter effect in three-dimensional topological insulator Bi₂Se₃ nanoribbons

Liu Genhua^{1, 2, †}, Xiao Pingguo¹, Xu Piaorong¹, Zhou Huiying¹, Zhou Guanghui²

(color online) Energy band structure for a Bi₂Se₃ nanoribbon with under an electric field with strength (a) 0, (b) , and (c) . (d) The band gap as a function of L_z ( ). The inset shows vs E_y (black dotted line) and E_z (red dash line). Spin-up and -down surface states are marked with up and down red arrows in panels (b) and (c), respectively.