What Happens to the Integer Quantum Hall Effect in Three Dimensions?
The integer quantum Hall effect is often advertised as one of the most striking phenomena to occur in the two-dimensional electron gas. It is nevertheless natural and interesting to ask whether it can also take place in a three-dimensional system, and that question is the subject of this article. More specifically, two remarkable aspects of the quantum Hall effect in two dimensions are that the Hall conductance shows plateaus, in which it is constant for a range of Landau level filling factors, and that, when the Hall conductance lies on a plateau, current flows through the sample via edge states. Here we ask, for three-dimensional systems, whether the Hall conductance can also show plateaus, and whether there then exist surface states, analogous to the edge states of a two-dimensional system. Of course, for there to be much to write about, the answers to these questions must in some circumstances be ‘yes’, and our focus will partly be on the conditions necessary to favour the quantum Hall effect in three dimensions.
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