Historians often label epochs of human history according to their material technologies—the bronze age, the iron age, and, most recently, the silicon age. From a physicist’s perspective, the silicon age began with the theory, experiment, and device prototyping of a new type of material: the semiconductor. Although semiconductors had been known since the late 1800s as materials with unusual sensitivities to light, direction of current flow, and method of synthesis, not until the early 1930s did Alan Wilson make the radical proposal to describe their conduction in terms of the filling of their electronic bands.1
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.