[PDF]    http://dx.doi.org/10.3952/lithjphys.51108

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 51, 53–63 (2011)

CONTROL OF TWO-DIMENSIONAL ELECTRON SPIN BY AN ABRUPT CHANGE OF PHYSICAL PARAMETERS OF A QUANTUM WELL
A. Dargys
Semiconductor Physics Institute, Center for Physical Sciences and Technology, A. Goštauto 11, LT-01108 Vilnius, Lithuania
E-mail: dargys@pfi.lt

Received 7 March 2011; accepted 17 March 2011

We apply Clifford algebra to investigate 2D electron spin reflection off and transmission through a stepped discontinuity of physical parameters in semiconducting quantum well. The discontinuity may be due to change of spin-orbit interaction constants, effective masses, or electrostatic potential. In the paper the posed problem has been solved exactly. It is shown that the reflected electronic beam has identical spin polarization as the incident one. However, the transmitted beam suffers spin flipping and in general case consists of a mixture of up and down spin states. Optimal conditions for total reversion of 2D electron spin polarization are found. Special attention is paid to correct boundary conditions in the presence of spin-orbit interaction. A simple formula that connects spin polarization of the transmitted beam and SO interaction constants is presented.
Keywords: Clifford algebra, geometric algebra, semiconductors, spintronics, spin polarization, spin flipping, quantum well
PACS: 85.75.-d, 72.25.Dc, 71.70.Ej, 03.65.Fd

DVIMAČIO ELEKTRONO SUKINIO VALDYMAS KVANTINIAME ŠULINYJE NAUDOJANT STAIGŲ FIZIKINIŲ PARAMETRŲ PASIKEITIMĄ
A. Dargys
Fizinių ir technologijos mokslų centro Puslaidininkių fizikos institutas, Vilnius, Lietuva
Suformuluotas ir išnagrinėtas elektrono sukinio atspindžio ir pernašos uždavinys, kuriame atsižvelgta į staigų fizikinių parametrų pasikeitimą, pavyzdžiui, sukeliamą sukinio ir orbitos sąveikos netolygumo, efektinių masių skirtumo arba potencinio laiptelio buvimo kvantiniame šulinyje. Uždavinys išspręstas pasitelkus Cliffordo algebros, dar vadinamos geometrine algebra, matematinį aparatą. Tiksliai išnagrinėtas atvejis, kai elektronas krinta statmenai netolygumo laipteliui. Parodyta, kad, nepaisant laiptelio savybių, atsispindėjusio elektroninio spindulio poliarizacija visada sutampa su krintančio spindulio poliarizacija. Tuo tarpu praėjusio pro netolygumą elektrono poliarizacija gali pasikeisti į priešingą. Nustatyta, kad bendruoju atveju praėjęs elektroninis spindulys sudarytas iš ordinarinės ir ekstraordinarinės bangų. Apibūdintos optimãlios poliarizacijos apvertimo bei spindulio depoliarizacijos sąlygos, kurias turi atitikti kvantinio šulinio medžiaga abiejose parametrų trūkio pusėse. Gauta labai paprasta formulė, kurioje yra tik sukinio ir orbitos sąveikos konstantos ir kuri leidžia nustatyti praėjusio elektroninio spindulio poliarizaciją. Taip pat gautos elektrono spinoro amplitudės bei jo greičio nenutrūkstamumo lygtys, kurios gali praversti tuo atveju, kai elektrono sukinio judėjimas nagrinėjamas klasiškai.

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