(n-2)-fold resonant splitting in open periodic quantum structures

We have calculated the conductance for two kinds of open periodic structures, using the lattice Green's function method. It is found that (n-2)-fold resonant splitting appears at energies slightly higher than the first threshold energy, while resonant peaks satisfying the (n-1)-fold splitting rule exist in the low-energy region of the conductance profile. The (n-2)-fold resonant splitting peaks are induced by high quasibound states in which electrons are mainly localized in the constrictions rather than in the stubs or junctions of the open structures. To this kind of quasibound state, the stub or junction acts as a potential barrier rather than a well, which is the inverse of the case of the quasibound states corresponding to the (n-1)-fold splitting peaks. It is also found that the number of high quasibound states existing in each constriction is related to the constriction length. In order to observe the (n-2)-fold resonant splitting, the constrictions between stubs or junctions in the open structure should be sufficiently long.