Origin of conductance quantization

It is well known that for an ideal one-dimensional conductor under ballistic transport conditions the conductance is transversally quantized in steps of 2e2/h as the constriction width is varied. We essentially obtain this quantization by invoking the uncertainty principle in conjunction with the definition of transport in the quantum limit. The finite resistance of a perfect conductor, which has been previously understood in terms of contact effects, can thus also be viewed as having a quantum mechanical origin in the uncertainty principle. Having analyzed the quantization using simple arguments, we observe that the quantized Hall resistance shows similar step structure, and hence may be similarly motivated. © 1998 Elsevier Science B.V.