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We address this question by implementing a self-consistent nonequilibrium Green\u2019s function (NEGF) calculation for a helical tight-binding model with spin\u2013orbit coupling and electron\u2013phonon interactions. The electron\u2013phonon self-energies are evaluated self-consistently, and the transport signal is extracted using the standard magnetization-reversal protocol with a spin-polarized analyzer lead. We benchmark a fully self-consistent NEGF within the self-consistent Born approximation treatment for both global and local electron\u2013phonon couplings against commonly used approximations, including diagonal self-energy schemes. We quantify how the resulting transport regime and spin polarization depend on phonon frequency, coupling strength, bias, temperature, and system size. In contrast to large polarizations and anomalous size trends reported under approximate treatments, the fully self-consistent calculation yields negligible spin polarization; in addition, the electron\u2013phonon coupling mainly renormalizes the spectrum and transport remains quasi-ballistic across the explored parameter range.<\/jats:p>","DOI":"10.1063\/5.0324706","type":"journal-article","created":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T11:24:53Z","timestamp":1776857093000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Weak electron\u2013phonon coupling is insufficient to generate significant CISS in two-terminal transport"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6166-4749","authenticated-orcid":false,"given":"Vipul","family":"Upadhyay","sequence":"first","affiliation":[{"name":"Department of Chemistry, Bar-Ilan University , Ramat-Gan 52900, ; , Ramat-Gan 52900, ; and , Ramat-Gan 52900,","place":["Israel Israel Israel"]},{"name":"Institute of Nanotechnology and Advanced Materials, Bar-Ilan University , Ramat-Gan 52900, ; , Ramat-Gan 52900, ; and , Ramat-Gan 52900,","place":["Israel Israel Israel"]},{"name":"Center for Quantum Entanglement Science and Technology, Bar-Ilan University , Ramat-Gan 52900, ; , Ramat-Gan 52900, ; and , Ramat-Gan 52900,","place":["Israel Israel Israel"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2643-9620","authenticated-orcid":false,"given":"Amikam","family":"Levy","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Bar-Ilan University , Ramat-Gan 52900, ; , Ramat-Gan 52900, ; and , Ramat-Gan 52900,","place":["Israel Israel Israel"]},{"name":"Institute of Nanotechnology and Advanced Materials, Bar-Ilan University , Ramat-Gan 52900, ; , Ramat-Gan 52900, ; and , Ramat-Gan 52900,","place":["Israel Israel Israel"]},{"name":"Center for Quantum Entanglement Science and Technology, Bar-Ilan University , Ramat-Gan 52900, ; , Ramat-Gan 52900, ; and , Ramat-Gan 52900,","place":["Israel Israel Israel"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,4,22]]},"reference":[{"key":"2026042207244729700_c1","doi-asserted-by":"publisher","first-page":"814","DOI":"10.1126\/science.283.5403.814","article-title":"Asymmetric scattering of polarized electrons by organized organic films of chiral molecules","volume":"283","year":"1999","journal-title":"Science"},{"key":"2026042207244729700_c2","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1126\/science.1199339","article-title":"Spin selectivity in electron transmission through self-assembled monolayers of double-stranded DNA","volume":"331","year":"2011","journal-title":"Science"},{"key":"2026042207244729700_c3","doi-asserted-by":"publisher","first-page":"4652","DOI":"10.1021\/nl2021637","article-title":"Spin specific electron conduction through DNA oligomers","volume":"11","year":"2011","journal-title":"Nano Lett."},{"key":"2026042207244729700_c4","doi-asserted-by":"publisher","first-page":"2560","DOI":"10.1021\/acs.accounts.6b00446","article-title":"Spin-dependent transport through chiral molecules studied by spin-dependent electrochemistry","volume":"49","year":"2016","journal-title":"Acc. 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