Quantum waveguide transport in serial stub and loop structures

We have studied the quantum transmission properties of serial stub and loop structures. Throughout we have considered free-electron networks and the scattering arises solely due to the geometric nature of the problem. The band formation in these geometric structures is analyzed and compared with the conventional periodic-potential scatterers. Some essential differences are pointed out. We show that a single defect in an otherwise periodic structure modifies band properties nontrivially. By a proper choice of a single defect one can produce positive-energy bound states in continuum, in the sense of von Neumann and Wigner. We also discuss some magnetic properties of loop structures in the presence of Aharonov-Bohm flux.