Conductance quantization in a periodically modulated channel

The transport properties of a quantum channel with a periodically modulated conducting width are investigated. A single constriction has a quantized conductance and its conduction plateaus have finite rises. For a short channel with just a few periods of modulation, conductance is no longer quantized. For a long channel with many periods of modulation, the quantized conductance characteristic of a simple quantum point contact is recovered, but the index of the quantization plateaus is no longer a monotonically increasing function. Rather, the conductance steps up and down with energy. We calculate the energy band structure of the corresponding infinite modulated channel. Comparison between the quantized conductance and band structure shows a one-to-one correspondence between the plateau index and the number of Bloch bands with positive group velocity at a given energy. The nonmonotonic conductance quantization for a long channel persists in the presence of an applied magnetic field, as does the direct correspondence between the plateau index and the number of energy bands. In the high-field regime this can be interpreted as selective resonant backscattering of edge states, and lends to nonmonotonic plateaus in the Hall resistance in the integer quantum Hall effect.