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In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. One demonstration of ballisticity is the quantized Hall conductance. Here we provide another demonstration of ballistic transport, in the way the edge states carry a supercurrent. The system we have investigated is a micrometre-long monocrystalline bismuth nanowire with topological surfaces, that we connect to two superconducting electrodes. We have measured the relation between the Josephson current flowing through the nanowire and the superconducting phase difference at its ends, the current\u2013phase relation. The sharp sawtooth-shaped phase-modulated current\u2013phase relation we find demonstrates that transport occurs selectively along two ballistic edges of the nanowire. In addition, we show that a magnetic field induces 0\u2013<jats:italic>\u03c0<\/jats:italic> transitions and <jats:italic>\u03d5<\/jats:italic><jats:sub>0<\/jats:sub>-junction behaviour, providing a way to manipulate the phase of the supercurrent-carrying edge states and generate spin supercurrents.<\/jats:p>","DOI":"10.1038\/ncomms15941","type":"journal-article","created":{"date-parts":[[2017,7,5]],"date-time":"2017-07-05T10:25:39Z","timestamp":1499250339000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":128,"title":["Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry"],"prefix":"10.1038","volume":"8","author":[{"given":"Anil","family":"Murani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alik","family":"Kasumov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shamashis","family":"Sengupta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu A.","family":"Kasumov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V. 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