At the time, the concept of energy bands was firmly established, but electron conduction mechanisms were not clear. In the view of Felix Bloch, whose theoretical work on atomic crystals underlies the modern understanding of conduction, metals and insulators were just opposite limits of a continuous electron itinerancy. Wilson instead proposed that band filling is the control parameter: A filled valence band allows conduction only through electrons that are excited across an energy gap to another band, whereas electrons in partially filled bands can readily conduct by scattering into nearby states.
Wilson and others recognized that bandgaps were often controlled by impurities, but how impurities functioned was poorly understood. (Wilson incorrectly speculated that silicon in its purest state was a metal.) The 15 years following Wilson’s proposal witnessed breakthroughs in purifying and controlling dopants in the elemental semiconductors silicon and germanium. Those advances eventually enabled the discovery of transistor action at Bell Labs in 1947. A surprise came, however, during the transistor patent preparation: The basic idea underlying the field-effect transistor had already been patented in 1930 by Julius Lilienfeld, an Austro-Hungarian physicist who had emigrated to the US in 1921.
For semiconductors, the path from theoretical understanding to device implementation was neither linear nor easily predicted. Topological materials seem to be following a similar trajectory. We have theoretical understanding and many ideas for novel devices, but ongoing materials development suggests the tantalizing possibility of our being at the dawn of a topological age. Here, we describe what it means for materials to be topological and how topology raises the prospect of revolutionary new devices.