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dc.contributor.authorHartmann, RR
dc.contributor.authorPortnoi, ME
dc.date.accessioned2017-09-21T09:51:40Z
dc.date.issued2017-09-14
dc.description.abstractWe obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Pöschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the eigenvalues are determined via the solutions of a simple transcendental equation. For the symmetric case, the eigenfunctions of the supercritical states are expressed as spheroidal wave functions, and approximate analytical expressions are obtained for the corresponding eigenvalues. A universal condition for any square integrable symmetric potential is obtained for the minimum strength of the potential required to hold a bound state of zero energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems are discussed.en_GB
dc.description.sponsorshipThis work was supported by the EU H2020 RISE project CoExAN (Grant No. H2020-644076), EU FP7 ITN NOTEDEV (Grant No. FP7-607521), FP7 IRSES projects CANTOR (Grant No. FP7-612285), QOCaN (Grant No. FP7-316432), and InterNoM (Grant No. FP7-612624). R.R.H. acknowledges fnancial support from URCO (Project No. 09F U 1TAY15-1TAY16) and Research Links Travel Grant by the British Council Newton Fund.en_GB
dc.identifier.citationVol. 7, Article number: 11599en_GB
dc.identifier.doi10.1038/s41598-017-11411-w
dc.identifier.urihttp://hdl.handle.net/10871/29456
dc.language.isoenen_GB
dc.publisherNature Publishing Groupen_GB
dc.rightsCreative Commons Attribution 4.0 International License CC-BYen_GB
dc.subjectTheoretical Physicsen_GB
dc.subjectDirac materialsen_GB
dc.subjectGrapheneen_GB
dc.subjectTwo-dimensional systemsen_GB
dc.subjectTopological insulatorsen_GB
dc.titleTwo-dimensional Dirac particles in a Pöschl-Teller waveguideen_GB
dc.typeArticleen_GB
dc.date.available2017-09-21T09:51:40Z
dc.identifier.issn2045-2322
exeter.article-number11599en_GB
dc.descriptionFinal published versionen_GB
dc.descriptionAlso available from Nature via the DOI in this recorden_GB
dc.identifier.eissn2045-2322
dc.identifier.journalScientific Reportsen_GB
dc.identifier.pmcidPMC5599532
dc.identifier.pmid28912569
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/


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