(color online) (a) Piezoelectric LiNbO slab with a line defect in the middle: three periods of honeycomb lattices are set up on both sides of the line defect and 16 periods of the supercells are arranged along the direction of the line defect (x direction). A pair of aluminium stripes (top and bottom electrodes) is set up on one terminal of the slab for inputting excitation signals. (b) A supercell of the structure, with w being the width of the defect.