Fig. 5: Results for Bi₂Se₃ in [001] direction with a twin boundary.

a The twin boundary structure along the [001] direction of Bi₂Se₃. The gray dashed line indicates the mirror plane M_z for this twin boundary structure. b The band structure of the slab geometry around the \(\bar{\Gamma }\) of projected surface Brillouin zone. The color of the dots represents the mean position of the states away from the mirror plane \(\left\langle \right\vert 2z/{L}_{z}\left\vert \right\rangle\), where the mirror plane is set at z = 0. c The mirror Hall conductance \({\sigma }_{xy}^{{M}_{z}}\) as a function of the chemical potential μ for several slab thickness L_z. d The dispersion of gapless Dirac bands. e The distribution of the mirror Berry curvature \({\Omega }_{{M}_{z}}({{\bf{k}}})={\sum }_{\chi }\chi {\Omega }^{\chi }({{\bf{k}}})\) for the four gapless Dirac bands. The region enclosed by the gray dashed line represents the first Brillouin zone.