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The state spontaneously breaks time-reversal symmetry and is sandwiched between two critical points, separating it from the broken time-reversal symmetry (BTRS) superconducting state at\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$${T}_{{\\rm{c}}}^{U(1)}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msubsup>\n                            <mml:mrow>\n                              <mml:mi>T<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mi>c<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mi>U<\/mml:mi>\n                              <mml:mrow>\n                                <mml:mo>(<\/mml:mo>\n                                <mml:mrow>\n                                  <mml:mn>1<\/mml:mn>\n                                <\/mml:mrow>\n                                <mml:mo>)<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                          <\/mml:msubsup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and a normal-metal state at\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$${T}_{{\\rm{c}}}^{{\\rm{Z2}}}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msubsup>\n                            <mml:mrow>\n                              <mml:mi>T<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mi>c<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mi>Z2<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msubsup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . We report a theory of the acoustic effects spectroscopy of systems with an electron quadrupling phase based on ultrasound-velocity measurements. We show that the experimental results are consistent with BTRS superconductivity at\n                    <jats:italic>x<\/jats:italic>\n                    \u2009~\u20090.8, fulfilling the necessary condition for the formation of electron quadrupling in Ba\n                    <jats:sub>\n                      1\u2212\n                      <jats:italic>x<\/jats:italic>\n                    <\/jats:sub>\n                    K\n                    <jats:sub>\n                      <jats:italic>x<\/jats:italic>\n                    <\/jats:sub>\n                    Fe\n                    <jats:sub>2<\/jats:sub>\n                    As\n                    <jats:sub>2<\/jats:sub>\n                    . We provide the theoretical basis and the experimental strategy to study the order parameter symmetry of emerging quadrupling condensates in superconductors.\n                  <\/jats:p>","DOI":"10.1038\/s41535-025-00819-7","type":"journal-article","created":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T14:25:09Z","timestamp":1764167109000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Ultrasound evidence for multicomponent superconducting order parameter in Ba1\u2212xKxFe2As2 with electron quadrupling phase"],"prefix":"10.1038","volume":"10","author":[{"given":"Chris","family":"Halcrow","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ilya","family":"Shipulin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Federico","family":"Caglieris","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongwei","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joachim","family":"Wosnitza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hans-Henning","family":"Klauss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergei","family":"Zherlitsyn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vadim","family":"Grinenko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Egor","family":"Babaev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,11,26]]},"reference":[{"key":"819_CR1","doi-asserted-by":"crossref","unstructured":"Grinenko, V. et al. 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