{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:59:22Z","timestamp":1776812362588,"version":"3.51.2"},"reference-count":110,"publisher":"American Physical Society (APS)","issue":"13","license":[{"start":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T00:00:00Z","timestamp":1713744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["ERC-2018-ADG-835105"],"award-info":[{"award-number":["ERC-2018-ADG-835105"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["URF\\R1\\211417"],"award-info":[{"award-number":["URF\\R1\\211417"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000271","name":"Science and Technology Facilities Council","doi-asserted-by":"publisher","award":["ST\/X000753\/1"],"award-info":[{"award-number":["ST\/X000753\/1"]}],"id":[{"id":"10.13039\/501100000271","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. B"],"accepted":{"date-parts":[[2024,3,26]]},"abstract":"<jats:p>An effective field theory (EFT) for dynamical axions in Weyl semimetals (WSMs) is presented. A pseudoscalar axion excitation is predicted in WSMs at sufficiently low temperatures, independently of the strength of the Weyl fermion self-coupling. For strong fermion self-coupling the axion is the gapless Goldstone boson of chiral <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><a:mi mathvariant=\"normal\">U<\/a:mi><a:msup><a:mrow><a:mo>(<\/a:mo><a:mn>1<\/a:mn><a:mo>)<\/a:mo><\/a:mrow><a:mtext>ch<\/a:mtext><\/a:msup><\/a:math> spontaneous symmetry breaking. For weak fermion self-coupling an axion is also generated at nonzero chiral density for Weyl nodes displaced in energy, as a gapless collective mode of correlated fermion pair excitations of the Fermi surface. This is an explicit example of the extension of Goldstone's theorem to symmetry breaking by the axial anomaly itself. In both cases, the axion is a chiral density wave or phason mode of the superfluid state of the WSM, and the Weyl fermions form a chiral condensate <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><c:mrow><c:mo>\u2329<\/c:mo><c:mover accent=\"true\"><c:mi>\u03c8<\/c:mi><c:mo>\u00af<\/c:mo><\/c:mover><c:mi>\u03c8<\/c:mi><c:mo>\u232a<\/c:mo><\/c:mrow><\/c:math> at low temperatures. In the presence of an applied magnetic field, the axion mode becomes gapped, in analogy to the Anderson\u2013Higgs mechanism in a superconductor. 't Hooft anomaly matching from ultraviolet to infrared scales is directly verified in the EFT approach. WSMs thus provide an interesting quantum system in which superfluid, non-Fermi liquid behavior, and a dynamical axion are predicted to follow directly from the axial anomaly in a consistent EFT that may be tested experimentally.<\/jats:p>\n          <jats:sec>\n            <jats:title\/>\n            <jats:supplementary-material>\n              <jats:permissions>\n                <jats:copyright-statement>Published by the American Physical Society<\/jats:copyright-statement>\n                <jats:copyright-year>2024<\/jats:copyright-year>\n              <\/jats:permissions>\n            <\/jats:supplementary-material>\n          <\/jats:sec>","DOI":"10.1103\/physrevb.109.134512","type":"journal-article","created":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T15:47:40Z","timestamp":1713800860000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Axions and superfluidity in Weyl semimetals"],"prefix":"10.1103","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1067-1388","authenticated-orcid":true,"given":"Emil","family":"Mottola","sequence":"first","affiliation":[{"name":"Deptartment of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9679-2409","authenticated-orcid":true,"given":"Andrey V.","family":"Sadofyev","sequence":"additional","affiliation":[{"name":"LIP, Av. Prof. Gama Pinto, 2, P-1649-003 Lisboa, Portugal and Instituto Galego de F\u00edsica de Altas Enerx\u00edas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5256-0822","authenticated-orcid":true,"given":"Andreas","family":"Stergiou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"16","published-online":{"date-parts":[[2024,4,22]]},"reference":[{"key":"PhysRevB.109.134512Cc1R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaa9297"},{"key":"PhysRevB.109.134512Cc2R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.crhy.2013.10.010"},{"key":"PhysRevB.109.134512Cc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.90.015001"},{"key":"PhysRevB.109.134512Cc5R1","doi-asserted-by":"publisher","DOI":"10.1080\/01422418608228774"},{"key":"PhysRevB.109.134512Cc6R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(83)91529-0"},{"key":"PhysRevB.109.134512Cc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.245147"},{"key":"PhysRevB.109.134512Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.100.201102"},{"key":"PhysRevB.109.134512Cc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.177.2426"},{"key":"PhysRevB.109.134512Cc10R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02823296"},{"key":"PhysRevB.109.134512Cc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.88.104412"},{"key":"PhysRevB.109.134512Cc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.85.165110"},{"key":"PhysRevB.109.134512Cc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.86.115133"},{"key":"PhysRevB.109.134512Cc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.87.161107"},{"key":"PhysRevB.109.134512Cc15R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.88.245107"},{"key":"PhysRevB.109.134512Cc16R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.111.027201"},{"key":"PhysRevB.109.134512Cc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.89.035142"},{"key":"PhysRevB.109.134512Cc18R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5037551"},{"key":"PhysRevB.109.134512Cc19R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-matsci-070218-010023"},{"key":"PhysRevB.109.134512Cc20R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-021-00310-9"},{"key":"PhysRevB.109.134512Cc21R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1630-4"},{"key":"PhysRevB.109.134512Cc22R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-020-0240-2"},{"key":"PhysRevB.109.134512Cc23R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0038804"},{"key":"PhysRevB.109.134512Cc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.103.235113"},{"key":"PhysRevB.109.134512Cc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.19.2227"},{"key":"PhysRevB.109.134512Cc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.38.1440"},{"key":"PhysRevB.109.134512Cc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.16.1791"},{"key":"PhysRevB.109.134512Cc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.40.223"},{"key":"PhysRevB.109.134512Cc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.40.279"},{"key":"PhysRevB.109.134512Cc30R1","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abj3618"},{"key":"PhysRevB.109.134512Cc31R1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/11\/10\/105008"},{"key":"PhysRevB.109.134512Cc32R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-nucl-102014-022120"},{"key":"PhysRevB.109.134512Cc33R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2020.06.002"},{"key":"PhysRevB.109.134512Cc34R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.122.345"},{"key":"PhysRevB.109.134512Cc35R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.124.246"},{"key":"PhysRevB.109.134512Cc36R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2021.115385"},{"key":"PhysRevB.109.134512Cc37R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.79.045014"},{"key":"PhysRevB.109.134512Cc38R1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-7571-5_9"},{"key":"PhysRevB.109.134512Cc39R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511803512","volume-title":"Dynamics of the Standard Model","author":"J.\u00a0F. 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