{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:43:11Z","timestamp":1760143391736,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,2]],"date-time":"2024-02-02T00:00:00Z","timestamp":1706832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Portuguese Foundation for Science and Technology (FCT)","award":["UIDB\/04650\/2020"],"award-info":[{"award-number":["UIDB\/04650\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>In the majority of experiments targeting nonlinear optical phenomena, the application of high-intensity pulses drives electrons in graphene into a strongly non-equilibrium state. Under these conditions, conventional perturbation theory falls short in explaining graphene\u2019s intricate optical response because of significant deviations in electron distribution over energy states from the equilibrium Fermi-Dirac one. In this work, we present a two-step relaxation model capable of predicting the transient dynamics of graphene\u2019s carriers out of equilibrium, from the generation of spectrally narrow populations of non-thermalized electrons and holes to the establishment of a hot-electron gas and its subsequent cooling toward equilibrium with the crystal lattice. By comparing our model calculations to experimental results, we demonstrate its reliability and relevance to pump\u2013probe experiments, providing insights into the pivotal role of hot electrons in comprehending ultrafast dynamics in graphene.<\/jats:p>","DOI":"10.3390\/app14031250","type":"journal-article","created":{"date-parts":[[2024,2,2]],"date-time":"2024-02-02T09:24:08Z","timestamp":1706865848000},"page":"1250","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Two-Step Relaxation of Non-Equilibrium Electrons in Graphene: The Key to Understanding Pump\u2013Probe Experiments"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4551-9343","authenticated-orcid":false,"given":"Diogo F. P.","family":"Cunha","sequence":"first","affiliation":[{"name":"Centre of Physics\u2014CF-UM-UP and Laborat\u00f3rio de F\u00edsica para Materiais e Tecnologias Emergentes (LaPMET), University of Minho, Campus of Gualtar, 4710-374 Braga, Portugal"}]},{"given":"Rui","family":"Dias","sequence":"additional","affiliation":[{"name":"Centre of Physics\u2014CF-UM-UP and Laborat\u00f3rio de F\u00edsica para Materiais e Tecnologias Emergentes (LaPMET), University of Minho, Campus of Gualtar, 4710-374 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4758-1151","authenticated-orcid":false,"given":"Manuel J. L. F.","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Centre of Physics\u2014CF-UM-UP and Laborat\u00f3rio de F\u00edsica para Materiais e Tecnologias Emergentes (LaPMET), University of Minho, Campus of Gualtar, 4710-374 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2930-9434","authenticated-orcid":false,"given":"Mikhail I.","family":"Vasilevskiy","sequence":"additional","affiliation":[{"name":"Centre of Physics\u2014CF-UM-UP and Laborat\u00f3rio de F\u00edsica para Materiais e Tecnologias Emergentes (LaPMET), University of Minho, Campus of Gualtar, 4710-374 Braga, Portugal"},{"name":"Department of Physics, University of Minho, Campus of Gualtar, 4710-374 Braga, Portugal"},{"name":"Theory of Quantum Nanostructures Group, International Iberian Nanotechnology Laboratory, 4715-330 Braga, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,2]]},"reference":[{"key":"ref_1","unstructured":"Boyd, R.W. (2008). 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