Fundamental research in condensed matter physics has driven tremendous advances in modern electronic capabilities. Transistors, optical fiber, LEDs, magnetic storage media, plasma displays, semi-conductors, superconductors—the list of technologies born of fundamental research in condensed matter physics is staggering. Scientists working in this field continue to explore and discover surprising novel phenomena that hold promise for tomorrow's technological advances.

An important line of inquiry in this field involves topology—a mathematical framework for describing states that remain stable even when the material is deformed by stretching or twisting. The inherent stability of topological surface states has implications for a range of applications in electronics and spintronics.

Now, an international team of scientists has discovered an exotic new form of topological state in a large class of 3-D semi-metallic crystals called Dirac semimetals. The researchers developed extensive mathematical machinery to bridge the gap between with forms of "higher-order" topology (topology that manifests only at the boundary of a boundary) and the physical behavior of electrons in real materials.

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