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Less known are tensor monopoles giving rise to tensor gauge fields. Here we report that tensor monopoles can potentially be realized in superconducting multi-terminal systems using the phase differences between superconductors as synthetic dimensions. In a first proposal we suggest a circuit of superconducting islands featuring charge states to realize a tensor monopole. As a second example we propose a triple dot system coupled to multiple superconductors that also gives rise to such a topological structure. All proposals can be implemented with current experimental means and the monopole readily be detected by measuring the quantum geometry.<\/jats:p>","DOI":"10.22331\/q-2021-12-07-601","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T14:32:52Z","timestamp":1638887572000},"page":"601","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Tensor Monopoles in superconducting systems"],"prefix":"10.22331","volume":"5","author":[{"given":"H.","family":"Weisbrich","sequence":"first","affiliation":[{"name":"Fachbereich Physik, Universit\u00e4t Konstanz, D-78457 Konstanz, Germany"}]},{"given":"M.","family":"Bestler","sequence":"additional","affiliation":[{"name":"Fachbereich Physik, Universit\u00e4t Konstanz, D-78457 Konstanz, Germany"}]},{"given":"W.","family":"Belzig","sequence":"additional","affiliation":[{"name":"Fachbereich Physik, Universit\u00e4t Konstanz, D-78457 Konstanz, Germany"}]}],"member":"9598","published-online":{"date-parts":[[2021,12,7]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"P. 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D 31, 1921 (1985).","DOI":"10.1103\/PhysRevD.31.1921"},{"key":"13","doi-asserted-by":"publisher","unstructured":"C. Teitelboim, Phys. Lett. B 167, 69\u201372 (1986).","DOI":"10.1016\/0370-2693(86)90547-2"},{"key":"14","doi-asserted-by":"publisher","unstructured":"P. Orland, Nucl. Phys. B 205, 107\u2013118 (1982).","DOI":"10.1016\/0550-3213(82)90468-0"},{"key":"15","doi-asserted-by":"publisher","unstructured":"T. Banks, N. Seiberg, Phys. Rev. D 83, 084019 (2011).","DOI":"10.1103\/PhysRevD.83.084019"},{"key":"16","doi-asserted-by":"publisher","unstructured":"N. E. Mavromatos, S. Sarkar, Phys. Rev. D 95, 104025 (2017).","DOI":"10.1103\/PhysRevD.95.104025"},{"key":"17","doi-asserted-by":"publisher","unstructured":"M. Montero, A. M. Uranga, I. Valenzuela, J. High Energy Phys. 7, 1\u201349 (2017).","DOI":"10.1007\/JHEP07(2017)123"},{"key":"18","doi-asserted-by":"publisher","unstructured":"V. Mathai, G. C. Thiang, Comm. Math. 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