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Matter"],"published-print":{"date-parts":[[2025,6,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Quasi-one-dimensional hole gas is achievable in a semiconductor Ge nanowire. The lowest two subband dispersions of the hole gas are just two shifted parabolic curves with an anticrossing at <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:msub>\n                              <mml:mi>k<\/mml:mi>\n                              <mml:mrow>\n                                 <mml:mi>z<\/mml:mi>\n                              <\/mml:mrow>\n                           <\/mml:msub>\n                           <mml:mo>=<\/mml:mo>\n                           <mml:mn>0<\/mml:mn>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula>. This peculiar low-energy subband structure manifests the existence of a strong \u2018spin\u2019 (pseudo spin)-orbit coupling. Based on the Luttinger\u2013Kohn Hamiltonian in the axial approximation, we show two sets of combined dispersions that not only isolated from each other but also with strong \u2018spin\u2019-orbit coupling are obtainable in the presence of strong magnetic field. Realistic calculations are performed for three representative nanowire growth directions [001], [111] and [110]. These results are further confirmed via constructing the low-energy effective Hamiltonian of the hole gas. We also calculate the external electric field induced spin splitting for comparison with the magnetic field induced spin splitting.<\/jats:p>","DOI":"10.1088\/1361-648x\/add3eb","type":"journal-article","created":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T23:02:23Z","timestamp":1746226943000},"page":"225303","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Hole subband dispersions and strong \u2018spin\u2019-orbit coupling in a cylindrical Ge nanowire"],"prefix":"10.1088","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1900-5998","authenticated-orcid":true,"given":"Rui \u674e","family":"Li \u777f","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2025,5,19]]},"reference":[{"key":"cmadd3ebbib1","volume":"vol 484","author":"Bir","year":"1974"},{"key":"cmadd3ebbib2","author":"Winkler","year":"2003"},{"key":"cmadd3ebbib3","author":"Sun","year":"2009"},{"key":"cmadd3ebbib4","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/0022-3697(57)90013-6","article-title":"Band structure of indium antimonide","volume":"1","author":"Kane","year":"1957","journal-title":"J. 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