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Phys.: Condens. Matter"],"published-print":{"date-parts":[[2026,9,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We study delay-dependent high-harmonic generation in a two-dimensional (2D) material modulated by two coherent phonons. In our first-principles calculations, two phonon modes are simultaneously initiated by displacive launch and a time-delayed probe is used to drive the HHG. We observe two robust enhancement windows (\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mrow>\n                            <mml:mo>\u223c<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    13 and\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mrow>\n                            <mml:mo>\u223c<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    50 fs) in the HHG plateau yield. Notably, these enhancements do not coincide with displacive extrema of either single composed phonon mode. Based on a minimal harmonic model, we describe this behavior involving the delay ordering and phonon-phase sensitivity. Through analysis of the phonon-enhanced excited-electron number and the k-selective photocarrier injection concentration, we reveal a complex phonon coupling effect: the out-of-plane ZO mode predominantly modulates the band gap, establishing the phonon-driven carrier-excitation baseline and the characteristic momentum-space distribution, whereas longitudinal optical-induced valley reshaping further enhances carrier accumulation near\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>M<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    and strengthens plateau emission at the optimal delays. These findings establish two-phonon mixing as an effective control knob for optimizing HHG in 2D materials.\n                  <\/jats:p>","DOI":"10.1088\/1361-648x\/ae9dd4","type":"journal-article","created":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T22:54:16Z","timestamp":1787612056000},"page":"355402","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Modulation of high-harmonic generation by coherent two-phonon dynamical coupling"],"prefix":"10.1088","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7982-6103","authenticated-orcid":true,"given":"Liang-Yu","family":"Li","sequence":"first","affiliation":[{"name":"Chinese Academy of Sciences"},{"name":"University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao-Shuang","family":"Kong","sequence":"additional","affiliation":[{"name":"Ludong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu-Qiang","family":"Liu","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences"},{"name":"University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0440-3750","authenticated-orcid":true,"given":"Yun-Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"Nanjing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi-Hong","family":"Yang","sequence":"additional","affiliation":[{"name":"Nanjing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0055-0200","authenticated-orcid":true,"given":"Gang","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Advanced Intelligence and Computing (IAIC)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3402-1577","authenticated-orcid":true,"given":"Liang-You","family":"Peng","sequence":"additional","affiliation":[{"name":"Peking University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao-Ping","family":"Yang","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wan-Dong","family":"Yu","sequence":"additional","affiliation":[{"name":"Nanjing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,9,4]]},"reference":[{"key":"cmae9dd4bib1","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1038\/nphys1847","type":"journal-article","volume":"7","author":"Ghimire","year":"2011","journal-title":"Nat. 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