Quantum waveguide transport with side-branch structures: A recursive algorithm

Electronic conductance of a quantum waveguide with side-branch structures is investigated. We introduce impedance factors for geometric and potential scatterers and develop a recursive algorithm. impedance factors for several basic unit structures, recursion formulas, and an addition rule are presented with the use of one-dimensional quantum waveguide theory. The impedance factor of a complicated side-branch structure can be evaluated from impedance factors of the individual parts contained in the structure as in the classical resistance-network calculation. This method makes conductance calculations simple since the wave functions of the structures are not required. With this method conductance properties of the quantum waveguides with different periodic side-branch structures (vertical structures) are studied in detail. Electronic conductance of these side-branch modulators manifests band structure with fast oscillating regions and inherent regions. As the number of repeat structures increases, the number of sharp peaks in the oscillating bands increases proportionally while the conductance profiles in the inherent bands remain unchanged. Comparison with the conductance of similar periodic structures along the main wire (horizontal structures) reveals that the oscillating bands and inherent bands of the vertical structure correspond to the transmission bands and forbidden bands of the horizontal structure, respectively.