{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,30]],"date-time":"2026-10-30T05:46:49Z","timestamp":1793339209533,"version":"4.5.0"},"reference-count":59,"publisher":"National Academy of Sciences","issue":"4","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001843","name":"DST | Science and Engineering Research Board","doi-asserted-by":"publisher","award":["CRG\/2023\/000826"],"award-info":[{"award-number":["CRG\/2023\/000826"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001409","name":"Department of Science and Technology, Ministry of Science and Technology, India","doi-asserted-by":"publisher","award":["SB\/SJF\/2019-20\/06"],"award-info":[{"award-number":["SB\/SJF\/2019-20\/06"]}],"id":[{"id":"10.13039\/501100001409","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":[[2026,1,27]]},"abstract":"\n Realization of unusual particle-to-wave-like crossover in phonon transport and understanding its fundamental structural origin can guide the design of materials with ultralow thermal conductivity. Here, we report such a crossover from particle-like phonon propagation to wave-like coherence with increasing temperature in the zero-dimensional (0D) metal halide, Tl\n 2<\/jats:sub>\n AgI\n 3<\/jats:sub>\n . Composed of discrete (Tl\n 6<\/jats:sub>\n I)\n 5+<\/jats:sup>\n and (Ag\n 3<\/jats:sub>\n I\n 8<\/jats:sub>\n )\n 5\u2212<\/jats:sup>\n subunits, the structure exhibits intrinsic lattice instability governed by Pauling\u2019s third rule where face-sharing of polyhedra drives Coulombic cationic repulsion causing local distortion of Ag atoms, as confirmed by synchrotron X-ray pair distribution function (X-PDF) analysis and ab initio molecular dynamics (AIMD) simulations. Anharmonic low-energy rattling of Tl is evidenced within the (Tl\n 6<\/jats:sub>\n I)\n 5+<\/jats:sup>\n framework. These structural disorders generate low-frequency localized and anharmonic optical phonons that hybridize with acoustic branches, strongly suppressing lattice thermal conductivity (\n \n \n \n \u03ba<\/mml:mi>\n l<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n ). Consequently,\n \n \n \n \u03ba<\/mml:mi>\n l<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n drops to ~0.18 W\/m.K at 125 K and remains nearly temperature independent, signaling a breakdown of the phonon-gas model, attributed to phonon localization and wave-like coherence, modeled using the linearized Wigner transport equation (LWTE). The phonon localization in the 0D crystal structure results in a crossover from populations conductivity (\n \n \n \n \u03ba<\/mml:mi>\n p<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n ) associated with particle-like phonon propagation to coherence conductivity (\n \n \n \n \u03ba<\/mml:mi>\n c<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n ) through wave-like tunneling, at 175 K. Our study reveals 0D structural confinement along with anharmonic local structural dynamics can enable particle-to-wave-like phonon crossover, establishing a pathway to mixed phononic regimes and suppressed thermal transport.\n <\/jats:p>","DOI":"10.1073\/pnas.2521353123","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T18:45:37Z","timestamp":1769021137000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":7,"title":["Anharmonicity driven unusual particle-to-wave-like phonon crossover leads to ultralow thermal conductivity in Tl\n 2<\/sub>\n AgI\n 3<\/sub>"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-7525-3932","authenticated-orcid":false,"given":"Riddhimoy","family":"Pathak","sequence":"first","affiliation":[{"name":"New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research","place":["Bangalore, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8593-5871","authenticated-orcid":false,"given":"Sayan","family":"Paul","sequence":"additional","affiliation":[{"name":"Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research","place":["Bangalore, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5552-4448","authenticated-orcid":false,"given":"Shuva","family":"Biswas","sequence":"additional","affiliation":[{"name":"New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research","place":["Bangalore, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5124-7455","authenticated-orcid":false,"given":"Swapan K.","family":"Pati","sequence":"additional","affiliation":[{"name":"Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research","place":["Bangalore, India"]},{"name":"School of Advanced Materials and International Centre of Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research","place":["Bangalore, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9119-2455","authenticated-orcid":false,"given":"Kanishka","family":"Biswas","sequence":"additional","affiliation":[{"name":"New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research","place":["Bangalore, India"]},{"name":"School of Advanced Materials and International Centre of Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research","place":["Bangalore, 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