{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:25:19Z","timestamp":1760149519640,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T00:00:00Z","timestamp":1692144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We analyze a ballistic electron transport through a corrugated (rippled) graphene system with a curvature-induced spin\u2013orbit interaction. The corrugated system is connected from both sides to two flat graphene sheets. The rippled structure unit is modeled by upward and downward curved surfaces. The cooperative effect of N units connected together (the superlattice) on the transmission of electrons that incident at the arbitrary angles on the superlattice is considered. The set of optimal angles and corresponding numbers of N units that yield the robust spin inverter phenomenon are found.<\/jats:p>","DOI":"10.3390\/sym15081593","type":"journal-article","created":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T09:57:02Z","timestamp":1692179822000},"page":"1593","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Rippled Graphene as an Ideal Spin Inverter"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7887-9305","authenticated-orcid":false,"given":"J\u00e1n","family":"Bu\u0161a","sequence":"first","affiliation":[{"name":"MLIT, Joint Institute for Nuclear Research, 141980 Dubna, Russia"}]},{"given":"Michal","family":"Pudl\u00e1k","sequence":"additional","affiliation":[{"name":"Institute of Experimental Physics, 04001 Ko\u0161ice, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0489-7858","authenticated-orcid":false,"given":"Rashid","family":"Nazmitdinov","sequence":"additional","affiliation":[{"name":"BLTP, Joint Institute for Nuclear Research, 141980 Dubna, Russia"},{"name":"Faculty of Natural and Engineering Science, Dubna State University, 141982 Dubna, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"021003","DOI":"10.1103\/RevModPhys.92.021003","article-title":"Spintronics in graphene and other two-dimensional materials","volume":"92","author":"Avsar","year":"2020","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"226801","DOI":"10.1103\/PhysRevLett.95.226801","article-title":"Quantum Spin Hall Effect in Graphene","volume":"95","author":"Kane","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"155426","DOI":"10.1103\/PhysRevB.74.155426","article-title":"Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps","volume":"74","author":"Guinea","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"041401","DOI":"10.1103\/PhysRevB.75.041401","article-title":"Spin-orbit gap of graphene: First-principles calculations","volume":"75","author":"Yao","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"161409(R)","DOI":"10.1103\/PhysRevB.79.161409","article-title":"Graphene with structure-induced spin\u2013orbit coupling: Spin-polarized states, spin zero modes, and quantum Hall effect","volume":"79","author":"Rashba","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1098\/rsta.2007.2157","article-title":"Electron scattering on microscopic corrugations in graphene","volume":"366","author":"Katsnelson","year":"2008","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"075422","DOI":"10.1103\/PhysRevB.77.075422","article-title":"Midgap states and charge inhomogeneities in corrugated graphene","volume":"77","author":"Guinea","year":"2008","journal-title":"Phys. Rev. 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B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"012035","DOI":"10.1088\/1742-6596\/1416\/1\/012035","article-title":"Spin transport in a rippled graphene periodic chain","volume":"1416","author":"Smotlacha","year":"2019","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Pudlak, M., Smotlacha, J., and Nazmitdinov, R.G. (2020). On Symmetry Properties of The Corrugated Graphene System. Symmetry, 12.","DOI":"10.3390\/sym12040533"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"18925","DOI":"10.1039\/D1NR06407J","article-title":"Spin selectivity in chiral metal\u2013halide semiconductors","volume":"13","author":"Feng","year":"2021","journal-title":"Nanoscale"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1016\/j.carbon.2018.11.076","article-title":"Modifying the electrical properties of graphene by reversible point-ripple formation","volume":"143","author":"Alyobi","year":"2019","journal-title":"Carbon"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"056807","DOI":"10.1103\/PhysRevLett.100.056807","article-title":"Periodically Rippled Graphene: Growth and Spatially Resolved Electronic Structure","volume":"100","author":"Calleja","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1021\/nn203775x","article-title":"Quasi-Periodic Nanoripples in Graphene Grown by Chemical Vapor Deposition and Its Impact on Charge Transport","volume":"6","author":"Ni","year":"2012","journal-title":"ACS Nano"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.carbon.2016.02.066","article-title":"Spatial variation of wear and electrical properties across wrinkles. in chemical vapour deposition graphene","volume":"102","author":"Zurutuza","year":"2016","journal-title":"Carbon"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"085330","DOI":"10.1103\/PhysRevB.64.085330","article-title":"Spin-orbit interaction of electrons on a curved surface","volume":"64","author":"Entin","year":"2001","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"206402","DOI":"10.1103\/PhysRevLett.88.206402","article-title":"Spin-Orbit Coupling and Electron Spin Resonance Theory for Carbon Nanotubes","volume":"88","author":"Egger","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1038\/nature06822","article-title":"Coupling of spin and orbital motion of electrons in carbon nanotubes","volume":"452","author":"Kuemmeth","year":"2008","journal-title":"Nature"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"235301","DOI":"10.1103\/PhysRevB.77.235301","article-title":"Spin-orbit interaction and anomalous spin relaxation. in carbon nanotube quantum dots","volume":"77","author":"Bulaev","year":"2008","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"235423","DOI":"10.1103\/PhysRevB.79.235423","article-title":"Curvature-induced anisotropic spin\u2013orbit splitting in carbon nanotubes","volume":"79","author":"Chico","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"075409","DOI":"10.1103\/PhysRevB.80.075409","article-title":"Curvature-enhanced spin\u2013orbit coupling in a carbon nanotube","volume":"80","author":"Jeong","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"074707","DOI":"10.1143\/JPSJ.78.074707","article-title":"Spin\u2013Orbit Interaction in Single Wall Carbon Nanotubes: Symmetry Adapted Tight-Binding Calculation and Effective Model Analysis","volume":"78","author":"Izumida","year":"2009","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"165427","DOI":"10.1103\/PhysRevB.84.165427","article-title":"Signatures of spin\u2013orbit interaction in transport properties. of finite carbon nanotubes in a parallel magnetic field","volume":"84","author":"Grifoni","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"085452","DOI":"10.1103\/PhysRevB.84.085452","article-title":"Carbon nanotubes in electric and magnetic fields","volume":"84","author":"Klinovaja","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1103\/PhysRev.71.622","article-title":"The Band Theory of Graphite","volume":"71","author":"Wallace","year":"1947","journal-title":"Phys. Rev."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Katsnelson, M.I. (2012). Graphene: Carbon in Two Dimensions, Cambridge University Press.","DOI":"10.1017\/CBO9781139031080"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Foa Torres, L.E.F., Roche, S., and Charlier, J.-C. (2014). Introduction to Graphene-Based Nanomaterials: From Electronic Structure to Quantum Transport, Cambridge University Press.","DOI":"10.1017\/CBO9781139344364"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"113846","DOI":"10.1016\/j.physe.2019.113846","article-title":"Spin-dependent electron transmission across the corrugated graphene","volume":"118","author":"Pudlak","year":"2020","journal-title":"Physica E"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2209137","DOI":"10.1002\/adma.202209137","article-title":"Graphene Spin Valves for Spin Logic Devices","volume":"35","author":"Ghising","year":"2023","journal-title":"Adv. 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