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The past decade has witnessed the emergence of a new frontier in condensed matter physics: topological materials with an electronic band structure belonging to a different topological class from that of ordinary insulators and metals. This non-trivial band topology gives rise to robust, spin-polarized electronic states with linear energy–momentum dispersion at the edge or surface of the materials. For topological materials to be useful in electronic devices, precise control and accurate detection of the topological states must be achieved in nanostructures, which can enhance the topological states because of their large surface-to-volume ratios. In this Review, we discuss notable synthesis and electron transport results of topological nanomaterials, from topological insulator nanoribbons and plates to topological crystalline insulator nanowires and Weyl and Dirac semimetal nanobelts. We also survey superconductivity in topological nanowires, a nanostructure platform that might enable the controlled creation of Majorana bound states for robust quantum computations. Two material systems that can host Majorana bound states are compared: spin–orbit coupled semiconducting nanowires and topological insulating nanowires, a focus of this Review. Finally, we consider the materials and measurement challenges that must be overcome before topological nanomaterials can be used in next-generation electronic devices. 

Exotic superconductivity, such as high TC, topological, and heavy-fermion superconductors, often rely on phase sensitive measurements to determine the underlying pairing. Here we investigate the proximity-induced superconductivity in nanowires of SnTe, where a s±is′ superconducting state is produced that lacks the time-reversal and valley-exchange symmetry of the parent SnTe. A systematic breakdown of three conventional characteristics of Josephson junctions -- the DC Josephson effect, the AC Josephson effect, and the magnetic diffraction pattern -- fabricated from SnTe nanowire weak links elucidates this novel superconducting state. Further, the AC Josephson effect reveals evidence of a Majorana bound state, tuned by a perpendicular magnetic field. This work represents the definitive phase-sensitive measurement of novel s±is′ superconductivity, providing a new route to the investigation of fractional vortices, topological superconductivity, topological phase transitions, and new types of Josephson-based devices.