(a) By applying the transformation matrix U1 (see Eq. (A1)) on the Hamiltonian of leads presented in Eqs. (3)–(5), (M−1)/2 equivalent ladder networks (black) and an independent chain (green) are achieved. (b) By applying the transformation matrix U2 (see Eq. (A2)), each ladder is converted to an equivalent PA-like chain with on-sites and hopping terms which are given by Eqs. (A6) and (A7). |