Ballistic electronic conductance of two parallel channels

For the ballistic motion of a two dimensional non-interacting electron gas at the Fermi momentum k the authors compute the quantum mechanical conductance (at zero temperature) of two narrow parallel channels of length L and lateral dimensions a and b. The basic global structure of the conductance reveals quantised plateaux of integer multiples of 2e²/h. The onset of each step occurs whenever one of the channels can populate a new subband. In the special cases where the relation k mod a-b mod =n pi (n=0, 1, 2, . . .) holds, the quantised steps are of two units. Experimentally, k mod a-b mod can be determined with some uncertainty (about 0.2 pi ) around certain values. Taking these uncertainties into account in our calculations, they find that the quantised conductance pattern is somewhat smeared and the two unit jumps become more profound. A closer inspection of the theoretical curves shows an oscillatory behavior which results mainly from longitudinal wave resonances in each channel, but interference effects between the two channels may also be present.