(color online) Schematics of HgTe nanoribbon in (a) open boundary condition and (b) periodic boundary condition in the width direction. The source and drain exist in the (pale green) filled regions. In both devices, a top gate voltage (a long trip shape) is embedded on the surface of the HgTe sample in the transport direction. The width of the ribbon and the circumference of the cylinder are set to be , where a is the lattice constant and N is the corresponding number of the lattices in the width direction.