Fig. 4: Results for Bi₂Se₃ in [100] direction.

a The slab structure along the [100] direction of Bi₂Se₃. The gray dashed line indicates the mirror plane M_x. b The band structure of the slab geometry along the high symmetry points of projected surface Brillouin zone: \(\bar{M}\to \bar{\Gamma }\to \bar{X}\to \bar{M}\). The color of the dots represents the mean position of the states away from the mirror plane \(\left\langle \right\vert 2x/{L}_{x}\left\vert \right\rangle\), where the mirror plane is set at x = 0. Red dot denotes the surface states and yellow dot represents the bulk states, and the blue dot indicates the mirror surface states. c The mirror Hall conductance \({\sigma }_{yz}^{{M}_{x}}\) as a function of the chemical potential μ for several slab thickness L_x. The accuracy of the Hall conductance is controlled by the precision of the numerical integral, which can be improved by increasing the number of k-points over the Brillouin Zone.