(a) Schematic diagram of the defect created for trapping Dwarf Dirac mode, (b) variation of normalized frequency fΛ/c with normalized defect radius (r_d/r) for obtaining the trapped mode resonating at the Dirac point. From panel (b), we find r_d = 2.511r for ε_a = 1, ε_b = 16 , and k_z = 0.50/Λ.