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dc.contributor.authorCulcer, Dimitrieeng
dc.contributor.authorHankiewicz, E. M.eng
dc.contributor.authorVignale, Giovanni, 1957-eng
dc.contributor.authorWinkler, R.eng
dc.date.issued2010eng
dc.descriptionURL:http://link.aps.org/doi/10.1103/PhysRevB.81.125332 DOI:10.1103/PhysRevB.81.125332eng
dc.description.abstractWe present a systematic derivation of the side-jump contribution to the spin Hall current in systems without band-structure spin-orbit interactions, focusing on the construction of the collision integral for the Boltzmann equation. Starting from the quantum Liouville equation for the density operator we derive an equation describing the dynamics of the density matrix in the first Born approximation and to first order in the driving electric field. Elastic scattering requires conservation of the total energy, including the spin-orbit interaction energy with the electric field: this results in a first correction to the customary collision integral found in the Born approximation. A second correction is due to the change in the carrier position during collisions. It stems from the part of the density-matrix off-diagonal in wave vector. The two corrections to the collision integral add up and are responsible for the total side-jump contribution to the spin Hall current. The spin-orbit-induced correction to the velocity operator also contains terms diagonal and off-diagonal in momentum space, which together involve the total force acting on the system. This force is explicitly shown to vanish (on the average) in the steady state: thus the total contribution to the spin Hall current due to the additional terms in the velocity operator is zero.eng
dc.description.sponsorshipWe would like to acknowledge stimulating discussions with S. Das Sarma, Jairo Sinova, Hans-Andreas Engel and Peter Schwab. D.C. was supported by LPS-NSA-CMTC. E.M.H. was financially supported by DFG under Grant No. HA 5893/1-1. Work at Argonne was supported by DOE BES under Contract No. DE-AC02-06CH11357. G.V. acknowledges support from NSF under Grant No. DMR-0705460.eng
dc.identifier.citationPhys. Rev. B 81, 125332 (2010)eng
dc.identifier.issn1098-0121eng
dc.identifier.urihttp://hdl.handle.net/10355/7631eng
dc.languageEnglisheng
dc.publisherAmerican Physical Societyeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. College of Arts and Sciences. Department of Physics and Astronomy. Physics and Astronomy publicationseng
dc.subjectspin polarized transport in semiconductorseng
dc.subjectspin-orbit couplingeng
dc.subjectZeeman and Stark splittingeng
dc.subjectJahn-Teller effecteng
dc.subjectmagnetoelectronicseng
dc.subjectspintronicseng
dc.subject.lcshSemiconductorseng
dc.subject.lcshElectron transporteng
dc.titleSide jumps in the spin Hall effect: Construction of the Boltzmann collision integraleng
dc.typeArticleeng


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