{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T05:44:57Z","timestamp":1792820697470,"version":"4.5.0"},"reference-count":30,"publisher":"National Academy of Sciences","issue":"46","license":[{"start":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T00:00:00Z","timestamp":1668124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100006445","name":"Center for Hierarchical Manufacturing, National Science Foundation","doi-asserted-by":"publisher","award":["DMR-2002850"],"award-info":[{"award-number":["DMR-2002850"]}],"id":[{"id":"10.13039\/100006445","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["651440"],"award-info":[{"award-number":["651440"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013368","name":"Deutsche Akademie der Naturforscher Leopoldina - Nationale Akademie der Wissenschaften","doi-asserted-by":"publisher","award":["LPDS 2020-01"],"award-info":[{"award-number":["LPDS 2020-01"]}],"id":[{"id":"10.13039\/501100013368","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2022,11,15]]},"abstract":"<jats:p>We present computations of the thermal Hall coefficient of phonons scattering off a defect with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon\u2013defect coupling is proportional to the phonon lifetime and has a \u201cside-jump\u201d interpretation. Consequently, the thermal Hall angle is independent of the phonon lifetime. The contribution to the thermal Hall coefficient is at resonance when the phonon energy equals a defect-level spacing. Our results are obtained for three different defect models, which apply to different correlated electron materials. For the pseudogap regime of the cuprates, we propose a model of phonons coupled to an impurity quantum spin in the presence of quasistatic magnetic order with an isotropic Zeeman coupling to the applied field and without spin\u2013orbit interaction.<\/jats:p>","DOI":"10.1073\/pnas.2215141119","type":"journal-article","created":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T13:35:08Z","timestamp":1668173708000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":38,"title":["Resonant thermal Hall effect of phonons coupled to dynamical defects"],"prefix":"10.1073","volume":"119","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1154-5236","authenticated-orcid":false,"given":"Haoyu","family":"Guo","sequence":"first","affiliation":[{"name":"Department of Physics, Harvard University, Cambridge, MA 02138"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Darshan G.","family":"Joshi","sequence":"additional","affiliation":[{"name":"Department of Physics, Harvard University, Cambridge, MA 02138"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2432-7070","authenticated-orcid":false,"given":"Subir","family":"Sachdev","sequence":"additional","affiliation":[{"name":"Department of Physics, Harvard University, Cambridge, MA 02138"},{"name":"School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2022,11,11]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1375-0"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-020-0965-y"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-020-18881-z"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.105.115101"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2208016119"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-32375-0"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.105901"},{"key":"e_1_3_4_8_2","first-page":"021025","article-title":"Evidence of a phonon hall effect in the kitaev spin liquid candidate \u03b1-RuCl3","volume":"12","author":"Lefran\u00e7ois \u00c9.","year":"2022","unstructured":"\u00c9. Lefran\u00e7ois ., Evidence of a phonon hall effect in the kitaev spin liquid candidate \u03b1-RuCl3. Phys. Rev. X 12, 021025 (2022).","journal-title":"Phys. Rev. X"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.82.1539"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.86.104305"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.167601"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.85.245107"},{"key":"e_1_3_4_13_2","unstructured":"M. Ye L. Savary L. Balents Phonon Hall viscosity in magnetic insulators. arXiv [Preprint] (2021). https:\/\/arxiv.org\/abs\/2103.04223 (Accessed 15 August 2022)."},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.104.035103"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.103.205115"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.105.L220301"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1080\/14786437208229210"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00660072"},{"key":"e_1_3_4_19_2","unstructured":"A. I. Krivchikov A. Je\u017cowski Thermal conductivity of glasses and disordered crystals. arXiv [Preprint] (2020). https:\/\/arxiv.org\/abs\/2011.14728 (Accessed 15 August 2022)."},{"key":"e_1_3_4_20_2","unstructured":"X. Q. Sun J. Y. Chen S. A. Kivelson Large extrinsic phonon thermal Hall effect from resonant scattering. arXiv [Preprint] (2021). https:\/\/arxiv.org\/abs\/2109.12117v1 (Accessed 15 August 2022)."},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.73.075318"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.75.045315"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.265901"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.55.2344"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.236601"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.101.045137"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1038\/nmat4360"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-020-0950-5"},{"key":"e_1_3_4_29_2","doi-asserted-by":"crossref","unstructured":"L. Mangeolle L. Balents L. Savary Thermal conductivity and theory of inelastic scattering of phonons by collective fluctuations. arXiv [Preprint] (2022). https:\/\/arxiv.org\/abs\/2202.10366 (Accessed 15 August 2022).","DOI":"10.1103\/PhysRevB.106.245139"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpr.2020.01.438"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2215141119","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T08:26:46Z","timestamp":1695284806000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2215141119"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,11]]},"references-count":30,"journal-issue":{"issue":"46","published-print":{"date-parts":[[2022,11,15]]}},"alternative-id":["10.1073\/pnas.2215141119"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2215141119","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,11]]},"assertion":[{"value":"2022-09-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-10-07","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-11-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2215141119"}}