{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T19:25:02Z","timestamp":1792178702645,"version":"4.4.0"},"reference-count":74,"publisher":"American Association for the Advancement of Science (AAAS)","issue":"12","license":[{"start":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:00:00Z","timestamp":1773792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.science.org\/content\/page\/science-licenses-journal-article-reuse"}],"funder":[{"DOI":"10.13039\/100006132","name":"Office of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006132","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Laboratory of the Rockies","award":["DE-AC36-08GO28308"],"award-info":[{"award-number":["DE-AC36-08GO28308"]}]}],"content-domain":{"domain":["www.science.org"],"crossmark-restriction":true},"short-container-title":["Sci. Adv."],"published-print":{"date-parts":[[2026,3,20]]},"abstract":"<jats:p>\n                    Chiral molecules, ubiquitous in chemistry and biology, can differentiate electrons by their spin, a phenomenon known as chirality-induced spin selectivity (CISS). Despite its robustness and technological relevance, CISS has resisted conventional explanation: Spin-orbit coupling (SOC) models cannot fully account for the observed magnitude, room-temperature persistence, or equilibrium signatures. Here, we argue that structural chirality enforces a twin-pair exchange mechanism via the indistinguishability principle, which intrinsically couples spin and spatial degrees of freedom such that wave functions cannot be factorized into spin and spatial components. We derive an effective Hamiltonian that describes both transport and equilibrium CISS phenomena and is non-Hermitian. However, the inherent pseudo-Hermiticity, with\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">P<\/mml:mi>\n                        <mml:mi mathvariant=\"script\">T<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    symmetry as a special case, ensures real eigenvalues and thermodynamic consistency. We demonstrate that our framework is a step toward resolving long-standing anomalies of CISS. It situates CISS alongside equilibrium symmetry-breaking phenomena such as ferromagnetism and superconductivity, with implications for spintronics, catalysis, and the origins of biological homochirality.\n                  <\/jats:p>","DOI":"10.1126\/sciadv.aec7069","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T17:59:43Z","timestamp":1773856783000},"update-policy":"https:\/\/doi.org\/10.34133\/aaas_crossmark","source":"Crossref","is-referenced-by-count":6,"title":["PT symmetry enforced twin exchange as the origin of chirality-induced spin selectivity"],"prefix":"10.1126","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4560-4225","authenticated-orcid":true,"given":"Pius M.","family":"Theiler","sequence":"first","affiliation":[{"name":"National Laboratory of the Rockies, Golden, CO, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8573-8673","authenticated-orcid":true,"given":"Sander","family":"Driessen","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Duke University, Durham, NC, USA."},{"name":"Department of Applied Physics, Eindhoven University of Technology, Eindhoven 5612 AZ, Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2711-1355","authenticated-orcid":true,"given":"Matthew C.","family":"Beard","sequence":"additional","affiliation":[{"name":"National Laboratory of the Rockies, Golden, CO, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"221","reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsnano.1c01347"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.chemrev.3c00661"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/adma.202106629"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.8b02196"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.108.218102"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.2c03224"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.5c01179"},{"key":"e_1_3_1_9_2","unstructured":"M. Gupta A. Grieder M. Fadel J. Simoni J. Yu R. Sundararaman Y. Ping The role of orbital polarization and spin-dependent electron-phonon scatterings in chiral-induced spin selectivity. arXiv:2508.03886 (2025)."},{"key":"e_1_3_1_10_2","doi-asserted-by":"crossref","unstructured":"M. D. Ventra R. Gutierrez G. Cuniberti Chirality-induced spin-orbit coupling and spin selectivity. arXiv:2502.09338 (2025).","DOI":"10.1021\/acs.jpca.5c05383"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.nanolett.2c01953"},{"key":"e_1_3_1_12_2","unstructured":"M. A. Haque P. M. Theiler I. A. Leahy S. P. Harvey J. Tan M. P. Hautzinger M. Taddei A. McConnell A. Greider A. H. Comstock Y. Dong K. Alberi Y. Ping P. C. Sercel J. M. Luther D. Sun M. C. Beard Chirality-induced magnetoresistance in hybrid organic-inorganic perovskite semiconductors. arXiv:2512.08046 (2025)."},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms14567"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.9b03487"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1021\/jacs.8b08421"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.nanolett.3c02483"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.ady4885"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adx4761"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.0c00474"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.nanolett.4c02912"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.9b02929"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.102.235416"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.nanolett.1c00183"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.196401"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.ado4285"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.166602"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41563-024-01838-8"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.283.5403.814"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1199339"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpclett.5b02419"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpcc.0c07372"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1002\/ijch.202200052"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-31096-8"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adw5850"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41560-024-01674-9"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201904206"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.aar4265"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adg8274"},{"key":"e_1_3_1_39_2","unstructured":"R. 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