**In his 18th century research on the fundamental nature of electricity, Benjamin Franklin found that there are two kinds of materials: conductors, in which electric charges flow freely, and insulators, in which charges are immobile. This discovery was of more than just academic interest: it enabled one of the most important inventions of his day: the lightning rod. Fast forward 250 years, and electronic materials like semiconductors, whose electrical conduction can be exquisitely controlled, now form the basis for the technologies that fuel today’s information age.**

**These capabilities were made possible by the ***20th century** revolution in our understanding of the structure of matter in terms of quantum mechanics. Insulators insulate through the concept of an energy gap—the barrier an electron must overcome to be dislodged. In a conductor, this energy gap is zero, which allows electrons to move freely. The foundations of the quantum theory of solids were established almost 90 years ago. Surprisingly, this theory contained a hidden treasure, whose significance was not originally fully appreciated. Insulators come in distinct varieties that can be characterized using the mathematical principles of topology. This new understanding has led to the development of new classes of **21st century** electronic materials.*

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