In Chapter 2, we introduced the idea of low-dimensional systems arising from quantum confinement. Such confinement may be due to a heterojunction, an oxide-semiconductor interface, or simply a semiconductor-air interface (for example, in an etched quantum wire structure). When we look at transport parallel to such barriers, such as along the channel of a HEMT or MOSFET, or along the axis of a quantum wire, to a large extent we can employ the usual kinetic equation formalisms for transport and ignore the phase information of the particles. Quantum effects enter only through the description of the basis states arising from the confinement, and the quantum mechanical transition rates between these states are due to the scattering potential. This is not to say that quantum interference effects do not play a role in parallel transport. As we will see in Chapters 5 and 6, several effects manifest themselves in parallel transport studies such as weak localization and universal conductance fluctuations, which at their origin have effects due to the coherent interaction of electrons.

In contrast to transport parallel to barriers, when particles traverse regions in which the medium is changing on length scales comparable to the phase coherence length of the particles, quantum interference is expected to be important. By “quantum interference” we mean the superposition of incident and reflected waves, which, in analogy to the electromagnetic case, leads to constructive and destructive interference. Such a coherent superposition of states is of course what leads to the quantization of momentum and energy in the formation of low-dimensional systems discussed in the previous chapter.