Quantum waveguide theory of serial stub structures

The electronic behaviors in quantum wires with serial stubs are studied. A general theory of quantum waveguide based on transfer matrix method is developed and is used to treat periodic stub structures, serial stub structures with a defect stub, and Fibonacci stub structures. A number of interesting physical properties in connection with electronic transmission, energy spectra, and charge density distributions in these structures, are found theoretically. In particular, we find that whether there are periodicity and symmetry in the transmission and energy spectra depends on the commensurability of the length parameters. If one length ratio is incommensurate, then the transmission and energy spectra do not exhibit periodicity and symmetry even for periodic stub structures. In particular, the quasiperiodic behaviors are shown in Fibonacci stub structures proposed by us whenever the length parameters are commensurate. The experimental relevance is also addressed briefly.